Maths-
General
Easy
Question
Hint:
Hint :- Using similarity of triangle ADC and AED we solve the given problem
The correct answer is: Hence proved.
Solution :-
Aim :- Prove that ![space A D squared equals A E times A C](data:image/png;base64,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)
Explanation(proof ) :-
Let ∠DCE =
then ∠EDC = 90° -
(angles of right triangle)
We know ∠ADC =∠EDC+∠ADE = 90° -
+∠ADE = 90°
So, ∠ADE = ![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
∠ADE = ∠ACD = ![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
∠ADC = ∠AED = 90°
![](data:image/png;base64,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)
By AA similarity
![straight triangle A D C tilde straight triangle A E D](data:image/png;base64,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)
By similarity we get
![fraction numerator A D over denominator A C end fraction equals fraction numerator A E over denominator D A end fraction not stretchy rightwards double arrow A D squared equals A C times A E](data:image/png;base64,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)
Hence proved.
Related Questions to study
Maths-
In the given picture, if AB = FE, BC = ED,
and
, then prove that AD = FC.
![](data:image/png;base64,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)
In the given picture, if AB = FE, BC = ED,
and
, then prove that AD = FC.
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that: ∠ABM ≅ ∠DCM
![](data:image/png;base64,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)
Prove that: ∠ABM ≅ ∠DCM
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASUAAACQCAYAAABOF30FAAAgAElEQVR4nO2dd3wUdf7/nzOzu1nS6DWUKKj0EnoTgSidAwSkBUKJCJ76Re/rnXfe19/p/X5+T9QDaTG0oDSl9yJIDb2JVClSRI7eElJ2Zz6/PzYzmYSACjFsks/z8QhkN7vZmczMa979owghBBKJROInqI97AyQSicSOFCWJROJXOB76ncLw/YcCKAjFfB4UBCjC98D6gXLPr1CUe5+TSCT5g8yBoXujRPe7/h9elDDSNUfF8MmQ74MAFYGC7tsQRUnfHoUMYbJ/L5FI8isi/V/F/owQ6Ze/SnY68AiilBkl/fNUQBUCn/WkZH2FbVOlKEkk+Zl0X8l3qZs6JJRfvPJzVpQAMHxfipMMj84gO/NNIpHkX4Tiu/IVfP8ohqkTNu8pG4V6BFFSMS0eFTAMAYaOqgkM4eXQd99z4vQ5GjaoT7ly5VBUBcU0pxDpDp+0liSS/ItACB1FUREGGAJUofgeC4GSvff2aNk3n3vm+63CSLeQdC+3r11j/Gef8fKwGKZOjeducopvQ3ybicgw7CQSSb5EIAwdRegYXg9C1xHCZznphoFh2HJgWcixkgAFgSoEisPByePHOH70GKFFS7Jy1RouXrqCbgibKElJkkjyNwretFTSklPwpqXi8aSSmpqKR9fRARz395JyKKYk0DQVRQgMbxpbN2/E7S7EyBEDGDduHHt27+HJJ8PJkCIpSxJJfmfdmtVMnzyVVK8XrwBVdVGnfgM6dOpE9Ro1KBEalO37HtpSMu0dRfgCWEL3gOLlp3NnWLN+M81bPEvP7l0oVaoY33yzlpSUFDxCQTd8Hym7WySS/EjGdX3k0CESduygZJkwqlevSfny5di6ZSsvvfQSf35rFOd//hkD8Bg+t87koS0loQhfCUC60aMoOihpnDx3hqPnrjK0Tn2eCC9Lm6b1WLV2A6dOnqFytao4FAWHoaAIAzQZ7JZI8iz24kR8hoaiZDwpjDTKPRHOX/75Ic+ULwvA9dt3mThhHBM+fB+Xy8W7//x/FAkOxiWEr5hSeSRLKaMwCgxQBZ40D9t37KRI8eJUrV4NVI22rVuRlHibb79dj+YARU2PvCuygFIiydcoAkMIklNTMBAIbyohwW7eGvUGw1+OYsHXX7Fv33doDp8MGene0yMEuu19Jb52kos/X2bu3AU0adyI6s9UAQwaNWtGhfLl2bhxI0l3UhCKrwpctphIJPkc38We/sBAKDpeIw2328Hz7VrgClDZs2cfXq+OYWS0nTxC75tqfZAidBCCnTt2c+HCf0CBFWtWY6TcQTN03AEBHD10mB+OnaBRw1oYhsBQQZW6JJHkW8yKxIxHBiqQZtylXIUyBIcG88MPP2CI9JJvASjKo4iSgjAUnygpOrrHy7q1G0lOSmXViuUsX7KAAA0cuoEwDC5du8WK5cto2KAWiqrZfE+JRJKfsZwiw8AQCpoGwUFBOFSNtNRUEALNlR7W4ZGLJwHVALxcvXyZHTv20LVrd3bt2cmuvXvYsWM7O3dtY+3a1dSqUZUN337Lz5eu+eJKMp4kkRQAjIw+EzQUxYmGmxs3kkhOTqVkyZJoqoquG5hdcQ8tSgqgKgoYXgQeFi1cwPVrtxgcPZRiRYpQvFgxihYvQZGiRalQvizde/Tg1Ikf2Lt3L05klZJEkv+xX+UqiuJAoKApLo4ePk1iUgp16tRG03xyZHpPj1bRLRRU1UFaqpfLV2/QsXNHGjduiGEYCGFg6AIdBTWgEM+1bkPdurW5m3jH52tKVZJI8jb3TaCbT6ooisClKKgoKA4XhZxOLl+5yrz5KwgKDKVB/Xrp2iUs7+mhY0qKku4rKm4cLgfDRryOQ3NSpEhQ+geooPnUUVFUatetS+zEcYQWDvUZcjL7JpHkK7KW+QjFiZGWzM+njxMg0vCkGZw89SNTp0xj0+bt/P3vf6fmU0/gVAxQVBACRVUfTZR8qGiai3Llwuw/9fmHNt1xBQTw5JNPZNkBiUSSX3G6Ajjz4zleeXk4Ae5C6LpAURyUKlWaD/7vhwzo1weXQwPDQACawydHOTZPSSKRSOxEPt8Wl9uJJ82LQOBwuHmmajXq1atHSOGiBDg1AAzDQLUVVSu5ucRSRiW3RCLJj5jXuBACRXjQdS+oKigKCmp6TZKKLgSaghVcFkLgcDhQHqlO6SE21jAMDMPwqaGioKpyMRWJJL+g6zrgC80YhoGKQNUcYI50VMwsG/iGQ5qPlUwGS666b4ZhoOu6JUhSlCSS/IMQAlVV8Xq9AL5xRkrma9wXC/dZR4oZeyZzjDnXRMm0kNxud259pEQiyUUcDgeGYaBpmm88NqqvwjpT94Z9llr2RkmuiZKmaSQkJDB+/HhcLpdlMT0opGU36+xW1S+9T+IfyOOU9zCP2a85buZrzSC1EILq1aszatQoW3o+va8tC/cZzw3ksvv2008/MXfuXKpWrUrbtm0pWbIkAF6vN5Pw2INl5tesWbP48ccfc3NzJY+I/WSV5B1UVaVs2bIUKlTIes7KjNmESFEUrl27xo0bN6yYcWRkJG+99RaaptkMCS3Tio/3DGLKQq6Kkqb5UoDnz5/n5s2bREVFUatWLdxuN16vF4fDkekkNgwDh8OB1+tl69at3L59m8DAQMtnlSe7/2IYBtevX8cwDIoUKUJgYKAVCJX4H6bQGIZBYmIiEyZMoEOHDpmOmWH45kNqmobH4+HIkSOMHj2axYsXWz8zhevBWfYHZ+BzVZQ8Hg8ASUlJzJ49m507d9KnTx/69u1L1apVrT+Kqqp4PB4rim+mC2fMmMHTTz9txadkoNx/uXjxIs899xxOp5PXX3+d6Oho65hK/A/TErpy5QqjRo1CURRcLpclNpBRT3T69Gnmz59PfHw8x48fx+FwULx4cW7cuJEj25KromRaNlWqVOHu3bucPHmSf/7zn2zatInBgwfTrVs3ihYtmslUNFUZoHLlyjz11FOy3ikPEBgYaB2nkiVLEh4e/rg3SfIrKFy4MIGBgdb1ZXfX7ty5w+rVq5k5cyYrV67EMAxKlChB7969KVKkCJ999lmOWMO5KkqO9DLyrl270qhRI+Lj41m/fj1btmzh8OHDbNmyhejoaJo3b25ZTfaiKlPUpCj5P16vV8aT8iDmNWcPoQDs27eP6dOns3DhQn7++Wc0TePZZ59l6NChdO/enY0bNzJ+/Pgc2YZcFSVTSIoUKULPnj1p2rQpK1eu5MMPP+TcuXNMnz6dzZs306VLFz744AOCg4MtV81+cmcttpJIJI+G3Tuxu2y6rjN+/HhiY2M5ffo0uq5TpEgR/va3v9G9e3eeeOKJHE9oPBb3zSyirFixIjExMTRu3JhJkybx1VdfcerUKcaNG8fu3bsZMWIEXbp0kbVNEkkuYXomaWlpfPvtt4wfP57Vq1eTnJxMUFAQnTp1sq5Z02gw35dTPJaGXNNETEtLQ9M0ateuzcSJE2ndujXjx49n//79JCQksH//fnr16sXw4cPxer1W9k4ikfw+mCITGxvLoUOHuHTpEi6Xizp16vDyyy/Tp08fihUrhmEYeL3e3yXZ9FjcNzNz5nQ6rZ8ZhkHv3r1p2rQp8fHxzJkzh1OnTjFjxgw2b95MUlISN2/etN7v8XgydxbLbJxE8puw96qpqsrVq1dZvXo1P/74o1UTWLp0aXr27MnIkSOpXr06kGEVmSU8Oc1jsZQeJCCVKlXi3XffpXXr1syZM4clS5bw448/omka7777LgMHDqRjx44UK1YMXdetP4oUJInk12NeN6b3sX79embOnMnSpUu5fv06gYGBtGrViujoaDp37kyhQoWskoBfrkN6NPxmnpIZYDPVu2XLltStW5dmzZoRHx/Pnj17+Oabb9izZw/bt29nwIAB1K9fH03TrGpS6d5JJL8Os9zm9OnTLFu2jM8//5yjR48CPqGKiYlh1KhRVKpUyZrukVs3/sfivkH2gTHz57quo+s6wcHBREVF0aRJE/r168fJkye5ceMGsbGxbNy4kf79+zNgwADKly+f6Xdmzc7JTJ2kIGJv14LM15/H42HZsmXExsayfft2EhMTKVKkCJGRkXz//fe0a9eOSpUq4fV60XUdVVVz7aafqz6P2R5i1rDYMZVb0zScTidOpxOPx4MQgvDwcIoXL86YMWMYMWIEbrebI0eO8L//+78MGDCA+fPnW6UDpqrb++Z0Xc+U5pRI8jvmue/1eq3rwfRCTp48yeuvv85//dd/8c0335CYmEijRo2YNm0a77//PqVKlbIKljVNw+VyZStIhmFYr7OHUh6VXLWUTPNvypQpLFu2zApU/xKKonDr1i1atmxp1TeNHz+evXv3smXLFo4ePcqWLVsYNmwYNWrUADJ6eczPlUV8koJE1qSSEIKbN2+yePFixo0bx6FDh9B1nTJlyhAVFcWrr75KpUqVuHr1KkWLFmXUqFG89957v+ozAK5fv87du3dzxsUTucjcuXMFICpWrCgOHjwovF6vSE1NzfYrJSVFJCcni6SkJHHr1i2RlJQkEhMTha7rQtd1cf78efH222+LsLAwAQhVVUVYWJiYMGGC+M9//iO8Xq8QQgiv1ysMwxCGYeTmrhZ4zp49KwAREBAgxo8f/7g3p8BhGIbweDxC13Vx+/ZtkZCQIDp06CCcTqcARGBgoGjXrp3YunWr0HVdpKWlieTkZJGamiqSk5NFYmKiSElJue/1ab4uLS1NXLt2TTRv3lwAIjIyUng8nke63h6LpeT1enE6nWiadt9Yj7C5X2ZjoL1Bt1y5crz//vu88MILTJ06lVWrVnHhwgXeeustVq5cSUxMDG3atCEkJAQgUxez+ftlnEmS17nfeWyGQ44fP87s2bOZMWMG586dw+FwEBERQXR0NL1796ZUqVKW62Uf0ma2dj3oGjGneDgcDsuNy4lr6rEVT9pdq+wwBcnE7tOKdNfM6XTStm1b6taty1dffcXcuXPZtm0bK1as4ODBg/To0YO+ffvSqFEjFEXJVJfxe6c1JZLfG/MGDZlvtpqmcf36dVatWkV8fDzffvsthmEQFhZGjx496NevH40bN7Zu8qZxYHf1ACv9/0vbkNNZuceWffs1r73f6+0D4HRdp3jx4owYMYJWrVoxa9Ys5s2bx8mTJxk7diybN29m4MCB9OzZk7CwMCuzJ8sHJHkde1+oKSS6rrNjxw5mzJjBkiVLuHz5Mm63m9atWzN06FDatm1LkSJFrIyaKSgPcz3YBSwnb/B+U6f0W7GLlvkHrlGjBu+++y7t27cnNjaWhQsXsn//fk6ePMmaNWsYOXIk7du3l2NaJfkC+yRIh8PBlStXmDBhAnPnzuXUqVN4vV7Cw8N57bXX6N69OxUqVACwuiH8lTwrSvZGQHusKTAwkJYtW/L000/Tpk0bJk2axL59+1i9ejWHDx/mxRdfJCYmhmeeeeYx74FE8miY7pXH42H16tVMnDiRDRs2kJKSQkhICF27duWVV16hQYMGBAQEZDuwzR/Js6Jk73uDe83HMmXKMHjwYNq0acPHH3/M4sWLOX/+POPGjWPt2rW8/fbbdO7cmeLFi1vmr31NOjOIJ5H4C+aN196mdfLkSeLi4pg+fTpXr15FVVXq1KnDa6+9Rr9+/aw528JWIuPvo3/y9FX3oJiTeVcIDw9n7NixdO7cmXHjxpGQkMCRI0d45ZVXeOGFF3jzzTeJiIggJCTEWsDAzFxIJP6GGci+cuUKq1at4pNPPuHQoUMYhkG5cuXo1asXr732mjXnyCTrteKvggR5XJQehL2kQAhBx44diYiIYOHChcTHx7N7926WLl3Kvn376NevH3369KFu3booipKp4tyfD56k4GC3dNauXcu0adNYvXo1t27dIiAggI4dOxITE2MN+zctf3910R5EvhUle9rfnP1SqlQpRo4cScOGDZk1axaLFy/m7NmzfPTRR2zdupXo6Gg6duxI2bJlrd+RFSlWkt+TB9UdnTp1iq+//popU6Zw+vRpVFWlbt269OvXj4EDB1K6dOnfbcZRbpKvRcn83z63CaBhw4bUqFGDrl27Mm7cONasWcO2bds4cuQIK1euZOTIkTRr1ozAwMBMwUH7unT2z5BIHhWR3qeW9ZzSNI3ExERWrlxpNc+mpqZSokQJevXqxbBhw6hVqxYOh8PKQuf1Grx8L0pZvzcJDAykefPmPPXUUyxdupS4uDgOHjzIkiVLOHDgAD169ODVV1/lySefvMedy8sHXOKf2NP79vNr7969xMbGsmLFCv7zn/+gaRpt27blj3/8I88++6w1Vyw/je7Jt6L0S5gHv3z58rz88ss0bdqUuLg4li5dypkzZxgzZgw7duxg+PDhdOzYkRIlSgAZGZC8biJL/BNzZdmzZ8+yaNEipk+fzqFDhxBCULlyZQYNGkRUVBQVK1YEMqZH5uUYUlYKtCjZTd569eoxduxY2rdvzyeffML+/fvZtm0bBw4coHv37rzxxhvUrl2bgIAAawSLvSzBn1OsEv8h63lif+xwOLh79y579uzh008/Zfny5ei6TmhoKK1ateKdd96xWqbMWKm9vSS/UGBFyS4o5vdOp5OuXbvSuHFj5s6dy+TJkzl69CizZs1i27ZtREVFERUVRZUqVQCs2U0msq5J8iDsdUamiJg3R/DVHE2ZMoWZM2dy4cIFABo1asSQIUPo1q0bpUuXziQ+9nM4P517+WdPHoKs9Uhm+UDZsmV54403aNmyJVOmTLHmhL///vts3LiRQYMG8eKLL1K4cGFrVZaswXSJxI7pXpmYrpbD4eDq1assXryYWbNmsXHjRsA3q75Pnz4MGDCAGjVqkJaWlq01nh+t8wItSlkxTxRd11EUhQYNGlC1alUiIyOZPHkyCQkJbN68mQMHDrBlyxaGDh1Kw4YNcbvdObJcsST/knVkjqZppKamsmvXLuLi4lixYoVVc/T888/zyiuvEBkZSUBAALqu5ytL6JcoOHv6KzCXCocMHz0oKIju3bvTvHlzFixYwJgxYzh16hTx8fFs2LCB6OhoYmJiKFOmzOPcdEkewB4quHDhAp9//jmzZs3izJkzADz99NO88cYb9OzZk2LFiqFpWqbMWn60irJDipINe42HvQRA0zTKli3LsGHDaNiwIVOnTmXBggWcPXuW0aNHs3nzZoYOHUqnTp0oXLiwNbsp63LG+SVlK/llhBB4PJ5Mc4pUVSUpKYl169bx2WefkZCQQFpaGsWLF6d3794MGTKEunXrZlpPzT5epKAgRSmdrI29We9KhmHgdDpp0KABNWrUsOJNe/bsYcOGDezdu5f+/fszaNAg6tSpk8mly0+ZEclvwwxCezwejh07ZgWyzbXVmjRpwsiRI+ncuTNBQUGZ3ldQkaL0K7FPrnS73bz00ku0bNnSWs33hx9+IC4ujnXr1jF06FD69u1LWFiY1UtXkGICkgwLW1VVLl68yKJFi5g8eTLff/89uq4THh7OSy+9xLBhwwgPDwfkiGYTeaX8BsyFL83iyQoVKvDOO+/Qtm1bZs+ezezZszlx4gT/8z//w4YNG+jbty89e/YkKChIBsILIJqmsXz5cqZNm2YtZeRwOIiKimLw4ME0btyYgICATOUBUpRyUJSyDubPrkDM/OPbfWZ7mjRrpfSD5iXlNvb2EvtJ5HK5aNmyJfXq1aNJkybMmDGDDRs2sGbNGnbv3s3OnTsZOHAgDRo0AMgUayoI6d38jL2637zpmAHpEydOMGvWLGbMmGEFshs3bsyAAQPo06cPJUqUyHTN+GP7kn2+WFbM89e+XiNgLVqZ3XvMuj77/mb3uhwTpawTIO3rjgNWJsHccBP79/YKVX9ePDI7oQwKCqJ///5ERkbyxRdfEBsby7lz54iNjbVcukGDBlGiRAmr+dLpdFontYw75T3M89Vc8FFRFKt59l//+hdHjx7F4/FQunRpoqOjiY6O5qmnngJ8I2nNFUP8FcMwuHnzJrNnz+bGjRsEBwcTEBBAcHAwbrcbl8tF4cKFMQyDO3fuAJCamsrBgwcpVKgQTqcTl8tlrXhi7q/L5bIW/siOHHXfTCvAnImdmppKUFAQbreb0NBQ9uzZY234gQMHSEpKspTW6XTicDisHTE32uVyWSvm+nP2ynTrwsLCePPNN3nuuecYM2YMq1at4sSJE7z//vusWLGCN998k/bt2+NyuTLNGPfHO6XkwZjWv3lj3bdvH//+979Zt24d165dIyAggE6dOvHaa6/RokULy423L3rhz7FGVVUJCQmhV69epKamWkaHWaZgCvGtW7dwu92A79q+cOECXq+XpKQkPB4PSUlJJCcnk5iYyN27d6lfvz6dO3fG5XJl+7k5+hcx63wqV67MkCFDSElJ4e7duyQnJ6MoCmfPngV8675dunQJVVWtpbnNA2xeoPaVGjweDw0bNqRWrVp+nx41h7I3bNjQWrxgxowZ7N69my1btnD8+HH69OlDVFQUtWvXziROkryB3XVRVZUzZ84wf/58pk+fzrFjx1AUherVqzN48GD69+9P2bJlrZle9uJJfz/upvVuzhfL+ry5L4mJiZbABAcH07p160whCnM/7ftvegnZ/g2yXaLyITAMQ+i6fs/KmPbVaRcsWCAAUa5cOXHixImc+mi/Qdd14fV6hdfrtVYnFcK3Wuybb74pypcvLwABiGrVqonY2Fhx4cIF6+9jX9U0r6/omx9WyLUfA/v57fF4hBBC3Lx5U6xatUq88MILQlVVAYjSpUuLPn36iJ07d97zPvu1kBeOsXn+mtuddT/Mr9u3b4vGjRsLQDz//PMiLS0t0zWQ9e9o/53ZkWOW0v3cD/tzZpwoayNrfiFrkN40c8PCwvjggw/o0KED06ZNY/ny5Rw9epT//u//ZtmyZQwZMoQXXniB4OBgyzI0VymVPB5ElrXUzPPYLGY8cOAAU6ZMYf78+Vy6dAlN06y11dq1a2cFsu+3oKO/W/yQsY0PSjaJ+yRs7rffvyZxJc/63wn7wRJC4Ha7iYyMpEaNGrRq1YqZM2eydetWVqxYwYEDB+jWrRtDhgwhIiJClg/4AVmr+s0L7fLly3z99dfMnj2bnTt3YhgGTzzxBAMHDqRXr15Uq1bNCn77cwzUn5Gi9DthzyLas5Jly5Zl6NChtGjRgi+++IJZs2Zx4cIFJkyYwLZt2xg6dCi9e/emZMmSj3kPCjZ2S0nTNLxeL5s3b2bixImsXbvWap7t3LkzI0eOpHnz5tasLSGHAD4S8i/3O2HeWc2qXnsth8PhoEaNGvzjH/9gyZIldO3aFUVR2L9/P3/729/o0aMHW7ZssVxcj8djuby6rmcazyvJGezutpkhM4tlr1+/zp///Gd69+7N/PnzuXXrFmFhYcybN4+4uDhat26Ny+WyZiM5HI48Ecj2V6Qo/c7cr0hMpA+Vi4iIYOrUqUyaNIk6depw9+5dtm7dSu/evXn77bc5fPjwPbVbdstLknOYwm/GQ27fvs3cuXPp0KEDY8eO5cqVK5QuXZrXX3+dtWvX0rFjR4oVK/bAwmHJb0e6b48ZXdcpXLgww4cPp02bNowZM4YVK1Zw9uxZPvnkEzZv3swrr7xCu3btKF26dKZ4hTz5cw67ZWsWAM6YMYMZM2aQmJhIUFAQTZs2ZeTIkXTq1AmXy5VJxOzxJ8mjIUXpMWLGLUyheeqppxg9ejQdOnRg8uTJbN26ld27d3P06FHat2/PsGHDaNq0KaGhodJK+h1QVZVz586xZMkSq3lW0zSqV69Ov379iIqKokKFCpYLrWlapiyyFKScQYrSY+J+o3gLFSpE586diYiIYMWKFUybNo0dO3Ywf/589u7dyx/+8Aeio6OpU6cOQLaLD8og670IW+uTXdBN1zo1NZVly5bxxRdfsGHDBhITEylcuDB9+/alf//+NGrUyIobmVaV+X773CwpTI+OFKXHiP0EznoylytXjujoaOrVq8ecOXOYO3cuP/74I5999hm7d+8mOjqabt26Ubx48XtaFqQrcS9ZOwbs4vLdd9/x5ZdfsmDBAs6cOYOqqjz77LMMGjSIbt26WXEj8z32m4mMI+U8UpT8FLOUoH79+jz99NN07tyZ0aNH880335CQkMDhw4dZvnw5b775Js2aNcsUY5Ku3b2YloyZUVMUhaSkJObMmUNsbCzHjx8nOTnZKtkYMGAAVapUQVXVfLEUdl5CipKfYroVHo+HwMBAWrduTbVq1Zg/fz6jR4/m3LlzLFu2jF27dtGvXz9GjRpFmTJlrLu4dCXuxf632b17N6NHj2bdunXcuXMHt9vNCy+8wN///nfq1atHUFCQ1f0PvoSEXLEmd5Ci5KfYR76AL3ZUqlQpRowYQevWrRk7dixLly7l4sWLfPLJJ2zZsoVRo0YRGRlpjUext0dAwYs1ZW0PEUJw5swZZs+ezdSpUy1XLSIigsGDBzNkyBAKFSpklVzYrSop8LmHFCU/JmubgnnXrlGjBpMmTeL5558nNjaWvXv3smvXLmuxzJiYGGrWrElQUFAmcSpIomTut1m0evHiRcs62rp1KwBhYWE899xz/OMf/6By5cqZ3p+170uSe0hRyiPYsztmb1yvXr1o3LgxCxcuJD4+noMHDzJ9+nS2bt1Kz549iYqK4plnnimQLp05TEzXdbZt20Z8fDyLFy/mypUrBAUF0apVK4YMGUL79u0JDAzE4/FI98xPkKKUR7AHsU33wuv1UrFiRd544w0aNGjAvHnzmD9/PidOnOCjjz5ix44d9OvXjx49elCsWLHHvAe5z/nz5/n666+ZM2cOe/fuBaB69epERUXRs2dPqlSpYtUcFRSxzgtIUcpD2NPPZiuEKVItWrSgZs2aNG/enKlTp7Jp0yY2bNjA999/T0JCAjExMTRq1AiHw3FP4Z897pJXMFP09vIHsxE2OTmZTZs2ERcXx/r1662ao65du5pFcg0AABGbSURBVDJ8+HDq16+P2+229l+OiPEv5NHIQ9hFI+ud3TAMQkND6datGy1atGD27NmMHTuWCxcuEB8fz8aNG4mJiWHo0KGULFnSajzNq4sdmtaiYRh4PB4CAgIwDIOffvqJ0aNH8/XXX3Pt2jWEENSqVYu//vWvtG/fnqCgIEuQ8+J+FwTkUckn2C2FsmXL8uqrr7Jo0SKGDRtG0aJFOXPmDB988AG9evViwYIFJCUlWdkle+o7L2FaiYGBgdy+fZv4+Hh69uxJXFwcV69epVSpUvzpT39i4cKFdO/enZCQEOt95iQAif8hLaV8hnnBuVwu6tevz2effUarVq0YP348+/fvZ8uWLezbt4+BAwcyaNAg6tWrh8vlsmaL55XYijnnOS0tjV27dhEXF8fMmTNJS0sjODiYli1bMmLECDp27JhppeK8bB0WFKQo5RPscSZ7XU1AQAD9+/enZcuWTJ06lTlz5nDy5EkmTZrE2rVriYmJoXfv3oSHh1uZvaxu4uNqW8nOerNXZZsD+2NjYzl9+jSqqlKvXj0GDhzI4MGDreV/7NXu5qo4BSkTmdeQopSPyK7Iz3xcsWJF3n33Xdq1a8fMmTOZPXs2p06d4u9//zvr1q0jOjqarl27EhISYg2RMy9mUxxyc7yrff1AM/5jGAYBAQHcvXuXRYsW8cUXX7Bx40bS0tIoVqwYgwYNYuDAgdSuXTvTSsbZIQXJf5GiVEAwXZhmzZpRrVo1mjRpwsyZM9m4cSPr1q3j0KFDbNq0icGDBxMREYHT6cyU7cvtmFPWTKP5/Z49e4iPj2fhwoVcvHgRl8tF+/btGThwIJ06dSI0NJS0tDRr9WJJ3kOKUgHCzFSFhobSr18/nn32Wb788kvi4uL46aefrFKCIUOG0L9/f8qXLw/cO2YlN7C7jJqmWQP74+LiOHLkCIZhEB4eTkxMDH379iUsLMwaQWJaVZK8iRSlAoIZGDZRVZVKlSrx1ltv0apVK2JjY1m6dCk//PAD7733Ht988w2vv/46kZGRBAYG3tNH93v1g9ndNfCtuLpz504+/vhjNm/eTGJiIoGBgXTv3p3XX3+dWrVqERAQkKmlBJCTOfMwUpQKCFljK2Ymyu1207x5c6pWrUpkZCRTp05l9+7drF+/nkOHDtGrVy8rS6eqaqZUek4XHXo8HitzqCgKR48e5csvv2TWrFmcP38eRVFo2rQp0dHRdO/ePdOKLzKbln+QolRAsS9GIISgWLFiREdH06ZNG8aOHcuCBQs4f/4848eP59tvv+Wtt96iffv2lCtX7ndbl05VVRwOB7du3WL9+vWMGTPGap4tX748nTt35k9/+hNPPPGEXBsvHyNFqYBipsTtqXGv10uFChX417/+RZcuXZgyZQqrVq3iyJEjvPrqq7Rp04aXX36Zdu3aERAQkOPbpKoq27dvZ+LEiaxYsYKbN2/idrtp164dw4cP59lnnyUoKAiPx5NpHyT5CylKBRT7bGkTs/3C5XLRpk0batWqRbt27Zg8eTIJCQmsXLmS7777jj/84Q8MGzaMevXqAdyzuoq9J82OvZkYMmYcKYrC5cuXiYuLY86cORw5cgSAiIgIoqOj6dmzJ2XLlrVcR4fDIQUpHyNFqQCTXbDaDBQbhkGJEiWsofkzZsxg7ty5nD17lkmTJrF9+3YGDx5Mjx49KFOmzD1rpt2v8NFc8NGMASUmJrJhwwbGjx9PQkICycnJlCpVihdffJEhQ4ZQt25dSyyzm40tyX9IUZLcFzPjVrVqVd577z26du3KRx99xNq1a9m/fz/Hjh1j+fLl/OUvf6FZs2ZWIDyrBWZiPud0OtF1nePHj/PZZ5/x1VdfcfPmTZxOJ02bNuWdd96hTZs21hRIs4hSToAsGEhRkmSLKQCmyxQQEEDTpk35/PPPWbRoEXFxcXz33XesXbuWI0eO8NJLLxEVFUX16tVxOBzZBqJN6+jy5cssWLCAqVOnsn//foQQVK5cmQEDBhAVFUV4eHimPjVTkCQFg1wVJbtJLzu0/R9FUTKl/YUQlCpVipdffplmzZoxbdo0Fi1axLlz5/j0009JSEhg8ODBdOrUybJy7NZNSkoKO3bsIC4ujiVLlpCcnEyxYsWIjIzklVdeoXnz5tbKs/b4VG4Xbkp+Hb/XNZyromTuhGnm25+T+B/3s04URaF27dp8+OGHtG3bls8//5xNmzaxY8cOvv/+e9auXUuXLl2sYkZVVTlz5gwzZsxg+vTpnD17FoCGDRsyZMgQXnzxRUqWLJntgo5Zt0GeL/6DefPI6WOSq6JkL3ArVKgQIAOWeZlChQrRpUsXmjdvzpo1a5gwYQIJCQksWLCAhIQEy8qZN28eX331Fdu2bSMtLY0yZcowcuRI+vfvz5NPPmn9Pnku5C1MC9bhcORoIe1jcd+Sk5OZNGkSJUuWlEVweRR7jZNpDVWqVIljx45x/fp1Ll26hKqqpKam8u2331rvczgcVKtWDSEEy5YtIy0tLdNij9ISyjuY54DX6+XixYtAzhy/x2Ip3bx5k3//+9/yzpjHMVP19hnf9sJGXdfvuel4vV62b9/O9u3b5Q0pj2OfbWU/7vY6tIdp/8lVUVIUhdDQUCtlLO+K+Y9fMy7kQYWVkryD/ZiZ4ZiQkJBsY4O/BUXkkjIIIfjpp584duyYXOhPIsmHCCEoUqQINWvWRFVVy63/reSaKJmNnzK9K5HkX+zr6KmqhsPx26/3XBMluLdOSY6bkEjyD/aQjK8tSEVVIGPRJAVExrfcx1HKVVGSSCQFBQHoIARgWktqhiilP8wO2WYikUh+JxQw48ZCsZ76JaQoSSSShyQftJlIJJL8gxBGphCRiX2ig6KoCMN8wa8rE5CiJJFIHgrDMDCEgaKAqqi22iTzfxWvnh78FgaqpqGl/9z3lX1QSYqSRCJ5CIQvXpRuBgmM9Ap/nRs3rqPrgsDAEIJDQtB1gdfrQdU0BAamKCn3ScFJUZJIJA+BgqoIhKIgDANFVTl8+BDz5i9g166d3LmdRIUK4Tzbqg09XuxOkSKhGJYQmaJkkJGZs/3mhy8JEJgK6XuoAl50/TbfHTjMwcOnfT6lIQgJDCKifgPCK4ejC997VYX0DZTkVwwhECK9D8qMJSgKQmScmooi0IWOIhQUI31uOAYoAhRVniN+jK57EUYqwvCyfPk6Ph0zlmu3rlK7Zk1CgkK4k5jCocNH6PNST0a99RYupxNVTXfvEKiKSnYu3CNYSsIWezdAqCiqh+TkH5kZP47JX6yjbHhFnMJL2u07BIcUZ+iIkQwaPBCnA5waODS5rHJ+RQiB1/CgqAqKAR6vnj7eQvPdxgSg63hJQ6gCBw5UQ8MwBIoGHsODpjrQVGnM+yuKAE2D4z8c5+PRY7hraHw6YTx1a1UjSC1MWpqXYz8c5tq1qwivF822Ao7vZvM7x5QMARoKhu7lxvXrNGnegn+O/l/KFyvMlZ8u8NFH/+aTj8dQtUYNnn+uKYaQHeL5GQFoioaqKHjxomgqAp/lY1pJoODQNFB0X3TBUMAA3WugOhQ0WfHvv4h0YVE11qxazY+nz/DxxM9p0qQJLhWcXjeBhaBRwwa+YDg+N8/XxfFg6zfnjnq6W6YovkZbd4CbkqVKU6p0aepFRNCnb19SUpM4e+6M7+WyjjyfY5Caepebt2/i8eqgOFCU9EZsQFVAVQUYBug6SXduc+3WbbyawJvemiBPET9GAUVTSb59g727dhMWVoF6devgdDp8JpQqMPSHmxaQY5aSVbhpjS1Q0TQHLs0BGICBIQRud2D66+VdMD+jez0smD+fzVsSqFajJr1e6kvZMqXTLWqBikDHwKEp7EzYxVfzF5FGANExMVR9ujJOVfVVAcuQkv+iwLXrV7nwn8sUL1aW0OBgDKGg4tMDzaliCHyWkqpYs5d+iRwWJV+gUlE1UlPSuH7tOoFGGudOHWPRovk0bBBBwwb1McTvVQsq8Rc8Hg/Lly3l63mLKVWuHMVLlaVPn5d8J6wQCAyEIki6dYtZ8TOYv2wFl26nUrNZM2rXeAbkfKU8gMDQvQhD913/ioKmaBleUPqCp5ry29bry/EoogI4HBrbt23n5WHDcYtkbl7+mStXbzB0xOsULlwYXaQb5/Kky7cIIXC7HNSrXwuhulm/cRPtOnakROEQXwpZEaiqwt7duzh26DD9+/bhy8UrSQW82LJ1Ev9E+Bpu3W43TqeLtFQPwkhfGETxpcEE4qGOY46LkgCEYfDUU08TPWQwJQIV9JREdu/ay+zZswgpUoKRr8QQHCgzb/kbBSEgrFw5qlStzcatO/jhhxMUqx+BA4GiQkpKMmtXrqZ44cI0atSI2ctXo6ugIy1pv0dRwDAoVrwoFSqWZ/Pmk1y6dJliZUPSkxkPJ0jwyIFu+4emn0bCia5DpfDydOnaiV69X6L/gCje+8f/oUP7F5gc9zmHDh9FU+WdMF8jDLxeD66AYJ57rhUpd26yZeNmklLT0NNDRT+fP8+Onbup37g+JUqFIgw9vYLFFyuV+DkKONyhNGrSlGs3LrF6zTekJKfgUlw4HE5QICU1ldt37vhq1iDT1/14aEvJEGpG94oAoaegKAZ4QkF3oShehDDwoqDgpGjxUtSvU5tZs77i2vXr6aWXkvyKogoMh0JKsot6tWoQ2bg2m9d8Q/e+UYSXD8Vh3GXr+m+5k+agyfOtUdVbYKThRMEBqNl1ekr8CkNoKKhEdujC6m+2MO7T97lz6xydO3ck0B3IlevXWbpsOaGFQ/nzn/9CYGCgFVPyVSkp2VpFOZACM1eySP9eKCiqL8ru0DSc+FY1uHj+LBs2baBChfKUKVdWmuf5HIEveeYVEBQaSotmTfjx+HGOHT6EhsLVi5dYsXwNNes0oGa9+niFOZVUwXjQL5b4FV6vQXilJ/jH+/+Hnr26s2jBAp5v+wKtW7cmetAgzp49S62atXCoGsL4dUf2oS0lJcsDYfhGFYj00vFD33/P5xMnUiQokJTEW+zbs4uDhw7z33/+K7VqPINXN3Bpsiwg3yIM0AVCqHgFNGvRggpl5rDwyy9p3yqCQ98d4/ip8/x54B8JCS6K7k1vW1IUS9CkleTfmFaPruvUrFmLjz/+hIMHD/Ldd9+RlpbGk5Wr0KBxY4oWKeIrBVAyLKMHeUo5EOj2nT2KqoJh4AwoRJ0GERw7d5FtmzehKSB0D09XqcyIkX+kSbMWPjGS1ZP5GgWBpggMBdK8OuWrPEPb51owMf5Ljh2KYfOm7ZQtX4GIBvXwCIGaXlxpGMIX6BYyO+vvmJewb40/LwEBATRq1IRGjZpYrzEAr9eTMV8p/fkH3XMe3lLKVNemgiIQBrgCQxg8LIYeL0XhRUMFHAoUDg0lODjEt6GGXF4p/5NeRIeKrmooKnRoH8mseV/z8cef8MPRU/To25cKlUqB4kEIUDHn7fgK7hCqFCY/RlVVFCVDQnzXtGEVSArhG4fr0ByI9AkBv6bBOmdLAlQFRWiEhhYjNNRxj4kmhPA1f2fsRo5+vMSfEKhGehcJKkL3Ur1OdSo9WZE58+ZRrWpd2raLRNMUVLxoQgddRzUECqApv9wjJXn8ZGdcZDxnv9KVLM/cn4cP6tyT11MRwtd0aSDQhQeBjoD0xxlBLgUhU775HSFwOzQC3G7QNHR0AkIL0ad/L4KLh1KnUSOeqfoUhgBFeAjQFILcAbgdDpzwq4OikvxHjllKZte3GcryjeRVfAUnAhSrj8mQPU0FAJerEL379eOWUpyQQgEIUhBC0LNPXxK1AKo9U4eQQoXwGAaKovFElWr87a9/pWat6maU8nHvguQx8fBD3jLVkZgeIxlhdTMIpqRbRYqvwlex/wIZL8i/2ALVvoGpRvp5kGGcGxjpNzHDLCzxPS98Q04AefPyax5cbZidtPyaWLJcjFIikfgVslBIIpH4FVKUJBKJXyFFSSKR+BVSlCQSiV8hRUkikfgVUpQkEolfIUVJIpH4FVKUJBKJXyFFSSKR+BX/H89jFmdGBQz8AAAAAElFTkSuQmCC)
Maths-General
Maths-
Prove that UZ = YZ
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAADSCAYAAAC1tgcDAAAgAElEQVR4nOydd3wUZfrAv1M2m96BBOmoFAEFFIRIUQQFPA88GyLFdlgQpKiopygqoiJgQ8UCiAUsHJwiTew/RBA44egiHZKQnmw22d2Z9/fHZobZBJSSZDdhvn5WNltnZ+aZ53mfKgkhBDY2NiGDHOwNsLGxCcQWShubEMMWShubEMMWShubEMMWShubEMMWShubEMMWShubEKOShFKUu9kEHwHoBB4PrexmfVgre51NqKCe3tsCD2LF/AMJSbKVcPVjvSj6BVIICSFU/9+yD0nIgAy6hCQJkDT/3/bxChlOUyhtaiJSuT/EiZ6zCSq2UNZqFCRJRpLAv1JxHNOIkv9/upCQJFskQ4lKE0ohRMDB1XUdWZYDnjf+tT5uU/n4jwVkHk0n/UgGQpORJA0kDSFJoDtwOJw0aNSQ6OgIBLamDCVOSyj98iUsfws0TTPvy7KKEMK8ybKMpmnmv6qq2oJZRei6QNd9KKrCJ598wjPPPIun2IsiAwroQqAoUcTGJDDt5en0v6YPCN2WyhCiUjSlpmlIkoQQAkVREMKvJSVJQtd1U2tKkoQsy3g8HsLCwmzBrHT8zhvjYnhZ2mU8+8zToMlIko6QfOhC4v33P2P7jj+gbP/rmo6i2sciVKgUodR1gdvtQpIkIiMjkSQZIUDoOkIIfD4fLpeLiIgInE4niqLY65gqwW+IKoqCrmu0aduGiy5qD0IByQf4WLv2V7Ky3uCav/WnU+eL0QFJsQUylDjDoyGQJB2n08GcObPp06cPK1auKguHCGQFNF1jxsszGDRoMLt27kII/3rTpmoQgC5AkhRkSUbzeUErBd1Hfm4WM2bMQA1zcM89d5OUFI9X07Bt19DitIRSIOM/kD7ADRTTs3tnsrKyeO21d8g8mouqakiyj/9u2si8Dz+iYZOmNGrSDKFLKLLD1pSVha6DriF0gQ7oyKCoCEkBSUWSVXRfMcJXykcfLODHH9cy4p6RtGrTGk0TyKLsM2xChjPSlBIChEBoXtq1a8t9997DL7+sZunSJYBMQVEhc+e+j+pwcNsdtxMTF+v3yOu6nfhTVZSFOiRkJCH776kKWzdv4a2353Bpl8u46aYbypYQAlUSyLJ9gQwlTk8oJQ0QIFQQESAiQYRxww3/oPUFTZk9+2127NjFTz+sYelXKxg8ZCgdO7RH1zUQOrIi2RZTZSFJlD+MQvh1JkJHkmSKij1Mf/0tCl2ljLx/FAnxsagyqJJ/+YHQgrLpNsfnNITSyKnUECiAAyEcCKHQoEF9HnpoJH/8sZ0Z019jxow3aNGiNdf/43ocYQ50XUNWBJJSJtQ2lYzwC6IoE8gyYftiyQoWfbmMe0eOovOllyA0UBAInw+5XHzZJviclvdVstwTQvJniej+XMuel3Xh6t6X8967s0mqW5/pM6bRsOE56DqoqoqEr+y9oR+yFkKQmZmJy+UiJSWF8PDwkA/jSAiE0PxLC1lm985tPD91Op26pHHdjdfjUBXQQSoLm+hCIAsl1A/FWcXpnWFCQkgyQgIhgyYEutDRNY3YmBiaNmqMx+clIjyCZs2aIUsSkgSSJJWlfdWMM0CSJP79739z6623snXr1hDdbsl/s26b0EHX8ZWW8PorL5ORcZTxDz9M03NSEAIUGWRFQVZUkJTA99oEndMQSmMNoyAkgS7pyKqOhhdFcbB7+16WfbWK7mndkRWJ2bPnUlBQjCyBX4oVvyTXgEtzdnY2S5YsITs7m/j4+GBvzl8jQEb4j5AE36xYyqKF/6Z7zx7USU5m684/2P37bnbs2MWOnb+TmZOHV8hl3nSbUOE0j4Y/Dgk6Ai8CD2FOBY+7hHffnoeroIRnJz/LjTdcz+LFi1n98y8oUFaZIAEKNUEo165dy+rVq7n11ltJTU0Nyfhq+QpWIQSS3z7lqy++ZE/6UT799BMu7XwpnS+5hIs7XkzHjpdwSafOvP3ubLxC8ufD2oQMp7ymFPjLYoWQURCowi+ckqTy4//9zLxP/s2oUaO4tMslJCfEs/KrJcx++03atm1JSv1Uf+6lDooSeCLoZdk/Bn5TVwr4+3hCUf515RPhT+m3WXJ1vV4v69atIzw8nO7duxMZGXmcutEQoewaKSGBpCApfnP2H7cM5ZzmLfAgI4SMjEDowr+alyW6dOmMU5ZqwOXxLEOcIroQwiOEKNGF0HVNCM0thKdIlBTmiO7du4mWrS8U237fLXTdI/QSt5j18quiblKymP76a8IldOHWdeF2e4Sm6YGfq+vC6/UKr9crdF2vcNM0Tfh8PqFpmtB1Xfh8PlFaWiq8Xq8QQghN0wKeMx4/FYzPF0KIjIwMcdFFF4nevXuLo0ePmttoY1PVnLJKkSw3PzIoCm+9NYvNmzYzZtwYGjdqhObTkVSVvv360bZtW955exa7du1CRiqrEjn2CUIIdF2ntLQUTdPMBHfrTZZlFEUxE9sVRSEsLAxV9St743HAfP5UkWXZTKBfv349mzZt4vLLLycxMRGv1xu6mtKmVnHmCemShO7TcIQ5ue+++7j22muQJX95l9AE9c85h7Fjx7Lkm6/JTE+nZbPmZQ6fYwkEkiSRmZnJ66+/TnFxMfHx8cTFxREeHk5kZCQRERFERkYSGRlJeHg44eHhOJ1OM8Hd6XSaj51Jsruu60iShKZpzJ8/n3PPPZfevXubFwZbKG2qA0mcxpmmldVTSoAsfAhNR5JlUBx4fZrf9adpyH5/A3KYikcSeHUNFRlFFyhqoPBs3LiRu+66i44dOxIVFUVubi4ejwefz1dBi/p8PhwOhymoVsGNjo4mKiqK2NhY835MTAwxMTFER0cTERFBWFgYDocDRVFQVRWHw2FqXID09HS6detGWloab7zxBk6n0yzilmX5hMIpLIF4Yw1cfl0sTiFYb7zfeI/xPlG29i2/nrapHZxR8oA/yqGA6g9xCKGjKGVOeUVGlgVSmXtQliVURUEVAkWqmGZXUFBAcnIyY8aMoWXLlng8HkpLS/F4PHg8Hlwul/lYSUkJRUVFFBUV4XK5yM/Pp7i4mKKiIrKzs9m/fz+lpaW43W6Ki4sDbkZ5mVVQDQGOjo4mLi6OgwcPcvjwYRISEjhw4ACRkZHEx8fjdDoDBMPcH2WCU97BZAiNz+crqzMNLAw3XgOBAmjFMO3/zPF1Oqa6TehymkKpY0iVKFthGvk5EiDQEZJsMVH9kikHtKEMPIHz8/NRFIXo6GgAU5v9lSYwTmJN00wPrtfrxe12m4JZWlpKcXExJSUluFwuCgsLycvLo7Cw0BTunJwcjhw5Qn5+Pj/88AMOh4Pt27czbtw4fD4fXq8Xp9Npat+oqCiio6MDNLAh2MbNML9jYmJwOp3IsmxqZUPrGhj3j/d7y7dVKS/QNrWL09aUIiBNzv+IH1H+hQHIFSJrfvLz85EkiYiICOBYzaX1JBSWkAVgmpKGY8fQGKqqEhUVVeGkNV6r6zqapuFwOCpsx/fff8/q1asZOHAgDzzwAG632xTc4uJiU5gLCgrIy8sjPT2d/Px80xFkNW+tzild11EUhdjYWOLj40lMTCQuLo64uDgiIyPNdbFV4KOionA4HKap7XA4kGXZdGrZQlk7OT1Hz3GErcKDkn89aT5FWRxNyPgrGERAeldhYSGKohAVFRWwXjLuW4Wx/NrN/Mqy+8brrHHN8mbn8cxKWZZZu3YtRUVF3HDDDbRu3fpPd4Mh3AA+n88UXMOsdrlcuN1utm3bxvTp02nevDklJSXs3r2boqIi3G43eXl55OXlmdrWcFhFRkYSFRVFRESEKcjx8fGmZo6LiyM6OtpcRxtr6oiICFOYjxw5Qt26dUlMTDS393j7zhbu0OI0va+yKU+Bh9NvwCrHXmY+rpS90t/hsGKaXWFhIU6nk7CwsMBP/BPhOxF/dbIZpqMhVIamzczM5Mcff6ROnTq0a9fuT78DMLUWgMPhMLV8eS644AI+++wzHn30US655BLcbjclJSVomsbixYt59913mTx5Mjk5OWzdupX9+/eTkZFBdnY2RUVFFBQU4HK58Hq9FUJEhpkfERFhalXDmZWbm0uzZs2YOHEiF110kemZNi5ChpAa2twmNKi2vq8VhTeQoqIicz0J1XP1tmph8KfVff/990yYMIE6deqckqf0z77D8PKGhYWZWsvg3HPPJTo6miuuuIK4uDjcbrd5oQDIy8sjMzOTrKwsXC4XRUVFZGRksHfvXg4ePEhubi4FBQXk5+eTm5tLUVERXq8Xn89fjbNt2zY2bNjAoEGDuO2222jZsiWKogTEgm1Ci5BpxlxcXExcXBxQ0TNZ1RhpdYaD529/+9ufhj5OBUmSCA8PJzk5mUOHDgGYJq+iKCQlJaFpGhkZGURGRpqhHuOCEB0dzTnnnPOn+8JwUh04cICdO3cye/Zstm3bRlhYGJqmER8fz7Rp01i1ahUjRoxg4MCBpKSkmK1BbcEMLYJisxgOG+vN7XaTmJhoCkN1BOqta9a9e/fy3Xffcemll5KamlppJ6sQgujoaBo1asSuXbsAAszIc889F0VR2LVrl+mVNTzJRlzWCIsYj1mdYLquEx8fT+vWrbnqqqtISUkhIyODa665hr/97W9ER0fz7LPP8vDDD3PkyBFGjhzJ3Xffzeeff05RUVHAtpR3qhmEYiJ+bSZoCwnrwdd1HZfLRVRUlHkCVNfVW5IkvF4vkZGR9OrVi+uvv76Cxj5djJPc6XTSunVr9u/fz9GjR83fLISgXr16dO3aleXLl+Pz+cxG1da1o/VmXf8ZwmTEMb/++mseeughGjduzOTJk7n66qtNh9akSZP46quvuPnmm1m8eDF33nknt99+u1knanyW1+s1LwTW+zbVyOkmzVYWRgL5gAEDxOzZs4UQwkwKr2o0TRMej8dMhM/LyxNFRUXC4/GYye1nis/nE0IIsW7dOtGvXz+xfPlyIYQQXq/XfG716tWiS5cuYu3atUKIY/vE5/Od9DasWbNGtG3bVnTp0kX89ttvQgghtm7dKho3bixGjhxpvi43N1csWLBA9OzZUyiKIlJSUsTDDz8stm3bFrBfjOT8ytoPNidP0MxXwxwz4oZFRUUkJSWZz1fXNljvGyEFOLbuq4zvEULQokUL6tWrx4oVK/B6vaY2FELQsmVLWrZsyaefforb7QaokKL3Z/zvf/9jwoQJhIeHM3XqVNq1a4eu66SmphIWFsaBAwfMz4yOjubGG29k/vz5PPPMM6SkpPD8888zaNAgZs2axcGDB02tbN0/NtVHSPjBS0pK8Hg8REdHV4rH82Swel0Nc9BIPjDWWZWxHf5u5ToxMTFcccUVbNy4kQMHDgRUpCQkJHDHHXfw22+/8dlnn5lmLHDCNZ7x9549e3jooYfIzc3lhRdeoGvXrvh8PjOuGxsbS0FBAR6PJyB5om7dujz00EPMnTuXsWPHkp2dzejRo7n77rtZuHAhBQUFx433ClE96/2zmmrXzWUYppEQQhw4cED06NFDrFmzxqyfrA7K12waj1XF9wghRE5Ojhg8eLAYO3asKC0tFR6PxzSVS0tLxcyZM0WPHj3E999/L3RdN01ro9bUamoLIURmZqYYPHiwaNCggVi5cqW5T42b2+0WAwcOFJ06dRI5OTlmXWr531hQUCC+/fZbMXjwYOFwOER8fLwYPHiw2LBhQ4Ap6/P5zO21qTqCZr7CMWdOTk4OqqoSERFRrbGz8jWb1m2q7O8BSEhIYNCgQaxatYrVq1cH5PbKsszQoUPp1asXjz/+OKtWrTI1ldfrNV8jhEBVVbKzs3niiSfYsGEDM2fOpGfPnvh8vgDHTHh4OM2aNTMTEI6XTA8QFRVF9+7defnll5k3bx7t2rVj8eLFDBw4kMcff5zt27cHdHSoLNPe5vgEzXy1mo/5+flmnaSo5eZRz549ufLKK5k+fToHDhxAVVUzzBEZGck999xD9+7dmTJlCosWLcLr9ZrCawiky+Xi+eefZ/ny5YwbN46rr766QjsVg/j4eFwuFwUFBUDFOaIGRmjlpptu4q233iItLY28vDxefPFFbrvtNmbNmsWBAwfMrCGbqiOoIRHjJMrNzSUsLIzw8PBaHcgWZeGR0aNHo+s6r776KkVFRQBmlk1iYiLjx4+nf//+vP7660ybNo0jR46Y7y8sLGT69OnMmTOHu+++m8GDB5vxTWsNp7Fvk5OTcbvdZGRkmJ9xokoUQ7ANjfzII48wduxYDh48yIQJE7jnnntYuHAhubm51bTHzlKq214W4thazggJvPfee+KGG24QR44cCXi8tmH8Nl3XxerVq0Xnzp3FCy+8YIY/rGEQt9stvvjiC9G7d2/Rt29f8fXXX4ucnBwxadIkERUVJUaPHi1yc3MD1sLGmtEablmxYoWIjY0Vc+bMEUKI464pjfWrx+MRQgixatUq0bVrV7F582ZRUlIifvjhBzFw4EDhdDpFUlKSuOWWW8TPP/8sPB5PwHcaNzuMcmYEJc2ufFW+VVMKi7extmlNa+ZMp06dePjhh3nppZdQFIV77rmHsLCwgLKyfv360aJFC9577z0mT56Mqqr88ssv9O3bl0ceeYTY2FizJOx4CftCCM477zyKiorYu3dvhecNjH1tpBv+8ssvXHDBBTRt2hSn00m3bt1o2bIly5cv57nnnuPnn3/m4MGDpKWlceutt9KiRQtzSvepdlewqUjQzFers6CgoMCsEKntKV3WNLqBAwfy8MMPM2/ePN58800KCwsD1o+aptG8eXOee+45/vGPf7Bq1SouueQSXnzxRZKTk80wx4kQZSl+iqJw+PDhgMfLv84QygMHDrB8+XJ69epFVFQUHo/HzJ8dMGAArVu35oEHHmDChAns27ePMWPG8Oabb3Lw4EGz7tNOdD8zgpaQbj1oLpeLyMhIwsLCKrTNqG1YC7N9Ph/9+/dHVVWmTJnCkSNHGD16tJl7C/79tHXrVhYuXEjHjh15/vnnadiwYYBWOh7G/nU6nbRo0YKjR49SWlqK0+k8bu8gTdOQZZkvv/wSn89Hjx49EELgcDjM53766Sfy8/Pp2bMn7dq1Iy0tjUWLFvHhhx+yYsUKhg4dSp8+fao13lwbCar31TgZjLItaxFzbUWSJDO/VVVVdF2nb9++TJs2jS1btjBixAh27NhhNvQ6dOgQd999Nzt37mTSpEl06NDB7EJgbbFp/XwjP1aWZcLDw0lLSyM9PZ2srCzzNbqum1rQELp9+/bx6aefMmTIEFJSUgLybzVN48cffyQlJYVWrVoBEBsby9ChQ5kzZw5XXHEFjz/+OMOGDWP9+vUBebmGSW79+2Qsop07d/LGG2+wZ8+eWm9BWQl6Ro/X66W0tJSYmJhqrRAJNlYt4vF4aN++Pa+++iqNGjXitttu49VXX2XTpk1MmDCBLVu28NRTT9G7d++AhP2TMRMdDgcXX3wxhw8fNoVS13V8Pp+5vx0OB8XFxUybNo3ExESGDRsW8BmyLHPo0CF++OEHevXqVaFRV2pqKvfeey/z588nNTWVe+65hwkTJpjxTeM7rVUvf4UQgpUrVzJx4kR+/PHHs6oIO+ia0uhUFxUVZT5+Nh0Aq1OmSZMmTJ06lbvvvpulS5cyePBgli1bxrhx47jppptOu2IjMTGR3NxcsrOzgWOjHURZ+MPj8TBnzhw2bNjA+PHjjxuHXLFiBcnJyfTo0aPChcAQvFatWvHaa6/x7LPP8scff3Dffffxxhtv8Mcff5j9hQzr6K9+R0FBAUuXLuX888/nsssuOysu1AZBP/s9Hg9ut5vIyEjg5DVAbcIqmKqqMnz4cMaMGUNJSQk33ngj999/f4U2KadCdHQ0TqeTwsJCILA7XmFhIe+88w4LFixg1KhRXHbZZRUuigcPHmTZsmVcffXVNGzYsIKAWLOhNE2jT58+vPnmmwwfPpwlS5Ywfvx4PvnkEwoLC0+6eHzLli389ttvXHbZZTRp0sQWyurA2MklJSW43W5TU55KdURtQwhBWFgY2dnZfPrpp/Ts2ZN//etfpmlvHc1wKiQnJxMZGWkG/Q3z848//uCRRx5hzpw5jBo1iuuuu8500GiahsfjQdd1vvjiC9xuN1dcccUJrRjrSAld10lMTGTo0KG8+eabdOvWjZdffpl//vOfrFmzxuw8aC3att7XNI2VK1dSXFxMz549T/t311SC3g7E5/PhdrvN/jyGKXS2mLDGxUnTNFRVJT8/nxdeeIHMzEyefvpp6tevD5zZ/jD6zu7atYs9e/awa9cufvjhB3766SdSU1OZPHky3bp1Mx06Rg5teHg4a9as4f333+f++++ncePGAVk/BuUtG8MvYJjk999/Pz179mT+/PlMnDiRTp06cdNNN9GmTZsKWUiKovDHH3/wzTff0K5dOzp06GB+1tkimEERSutBNTyAhlAer43k2YARuH///fdZvXo1Tz75JK1atTqj0X4GYWFhxMbGsmjRIrZu3YrL5SIxMZEhQ4bQr18/kpKSAkI1xro+Ozubl156iTZt2tC3b18zXHUy3QQN4TW2v0OHDlxwwQV89913fPTRRzz66KNcddVV/P3vf6dRo0bAsQvy1q1b2bVrF6NGjSI5Ofms6yMUNE1pHFyXy0VYWJhpvlpPjrMBa87qp59+yqJFixg7dizdunWrtO9ITEykffv2bN68mUGDBtG8eXOaNWtmTqcuH/OUZRmXy8ULL7xAYWEhzz33XEDs8WQvElZPsVEjetVVV9GxY0eWLl3KwoUL+e6777jxxhvp06cPCQkJlJaW8v333xMWFsZVV11Vodj6bDgvgppmB+B2uwkPDw/ojF6bd7zVVDPWSrIs88MPP/Dmm29y0003md30KiM2J4QgJiaG1q1bs3XrVrp37252srNWlli1JMCsWbNYtWoVM2bM4LzzzgsQsL8SDms/WeN3WrtM1KlThyFDhtC7d28++OADpk2bxpdffsno0aOJiIhg6dKldOrUiaZNmwZcCGrzeWEl6GvK4uLiAKE8G9aShmYyTLtt27bx3HPP0atXL26//faAmZtninEi16lThz/++IMjR46YQml93jj58/LymDlzJkuXLuXJJ5+kW7dux11D/hnH2+7jDSFKTU1lzJgx9OnTh3nz5vHggw+aTaT79u1LfHz8CUvSajNBT7MrLi422/TXdgyHhaE5ZFnm4MGDPPnkkzRt2pSRI0eaZnxlfqckSaSmplJaWmqGRaxeViMLaNeuXbzyyits2rSJxx57jKuuugqfz2c+X5lYLaILL7yQFi1asGLFCh544AGKiorYs2cPBw8eNHveGo6ws4GQCIlEREScsOV/bcIaz1MUxfS05ufn88gjj5CYmFjp6WTGd55zzjmkpKSYCQQGiqKQm5vLxx9/zH333UdmZiYvvfQS/fr1A6o25dH4bJ/Ph9Pp5MILL0RVVVq2bMl///tfRo4cyWeffUZ+fn6VbUMoEjTvq3GyuFwuc2RcbeR4FRlCCHw+Hy+99BI///wz7733Hk2aNMHj8VSZNkhISCAhIcFsCK1pGgUFBfzf//0fb731FhkZGdx///1cc801psfTKAurCqy5z4bVMHv2bPLz83nqqafo0aMHH330Ec8++ywLFy7k4Ycfpl27dsfNj65t5WJBc/QYSdBFRUVERUXhdDqDsSlVjtVkNe5rmsZ7773HkiVLmDx5Mm3atDFzUavqxHI4HMTFxfHtt98C8Pvvv7N9+3YUReHyyy/n+uuvp2XLluZ2WkcLVhWGIDkcDgoKCvj2228599xz6d69O/Xr12f8+PFcddVVzJ49m3vvvZdLL72UO++805yGZgjzn402rIkEzUg3dmZhYSHR0dG15ipnxRr0Nv5VVZWvvvqKmTNn8uijj3L11Vfj8XiqPLUwPDycevXqsXTpUmJiYqhbty7Dhw+nb9++pKammhcLY7urWiCtSQOSJLFp0yZ2797NsGHDSElJMc34tm3bMmXKFL777jveffddRo4cycCBA7nhhhsC5qHUJoKaPFBaWkpeXl6FSVS1DWu4YfXq1Tz99NMMGzaM66+/3rQYqjIUpGkaERERnHPOOXTu3Jm33nqL+Ph4UzAMZw5QKckKJ4sxHxRgyZIl5Ofnc+WVV5r9ioxtVxSFPn360LlzZxYtWsT8+fPN+s3evXsTHR1dYfZmTSao8QePx2Oar7UdWZbZvXs3L7zwAh07dmTEiBEB2qj87MjKwloK16BBAzODyhBIq2PJGh6pSgztZpjIhw4dYt26dVx66aW0bdvWHONn3XZN04iJiWHIkCG89dZb9O7dmylTpjBixAjWrFlTjQKpc7xJ5JQ9KoxJ5ebAcoFAR5QNSg6YYy7K3coIqo+5pKSEnJwcYmJigrkZVYY1n/Pw4cNMmjSJhIQEnnjiCXOYUflOC1VxYhmf2bx5czweD/n5+SQlJQUE5avigvBn22PtK1S/fn2mTp2K1+s1M4esA3mt2yZJEo0aNeL+++/niiuuYN68eUycOJH27dszZMgQ2rZtiyzL+Hy+APO4chIQNNB1BBJIMqKcTtMRCElDFjKK5v8eTfGhSz5kZBShogsJXRYoAmRTGCWQJHQhgRQkTWnsGK/XW6s1pXH1zs/PZ8aMGbhcLsaOHUvdunVN86z8iVMVGCd38+bNzTHw1m20nvDVVTZn/Q5FUbjwwgvp2LFjhalj1jCS9T2SJNGmTRueeuopxo8fT3p6Og8//DCvvfYae/furSDU5b/zNLe67P+GNOllN8zHA3Whcd8/4dx/t/yFTzr2UkAESygNSktLK0xwrk1IkkRxcTHvvvsu69evZ/To0bRp0wav12umuVW1AFjbcjRo0ACHw0F6ejpw7IIQjCyq8lrZOvDpZDHyaXv37s20adO49dZb+fbbb836zfJd4c/cEvBrSCS5TMyEKWMCEJKMhOwXWskHkgbICBzoyOiSQOZQRVQAACAASURBVEJHFsIUb78IyghJQpT99KCOLSgtLaW4uLjWakqAL774go8++oiRI0eSlpaG1+sN8MZWl1Yy2n7ExcWxb98+8yQ92X45VcHxzHZrLu5fYazJjSbWt9xyCy+//DJpaWm8+uqrjBkzhp9//tlcQlSGphSG5CCQhI4kg2woOwESUpkm9QEaiqQCCn7hFEhCIJf9iyyD4teOZb8aEMGLU4I/cUCSpFqVzWM4KVRVZfny5cyePZu77rqLvn37mqli1e0htJ7gycnJ7N271zxRgyWQ5feBYW6Wz7P9q88wnEXGb2zYsCEjR46kZ8+efPDBB0ycOJEOHTowbNgw2rZtazqZrOvo8iVrf4aQZED3C5XQKcgrpLjEQ2x8IkKWCVMVhK4hRAnF7lLyXRrh0fGERzhxCA1J0pGQ8fh0ilyFKIqD6JgohAS60Mv0ZhBxu92oqkp4eHgwN6PSsMbMfv31V1599VW6du3KkCFDCAsLq+BYqU7hNE7alJQUfv/992qfmP1XnKxQnOh9VgGTZZn27dvz3HPPMXbsWA4dOsSDDz7I9OnTzfmb1mwig7/SzqajVAckgRA6Xy5exOj772fbjp1IslxmzurIso/1637mn/+8hy+XrETXJSRZAkkgSYKso9mMG/8gCxd/AZLf0YPQkYO9pnS5XKiqWqvMV0VR2L9/P5MnT6ZJkyaMGjWKyMhIs1lUdVc8lK/aT0lJISMjg9LSUvP5UBHMM8X6O4z4b//+/Zk5cya33HILy5cvZ9SoUXz++efk5eVV8Dz/1X4wXDtCEiAEkiwhS/Dtt9+w8utVKKqMEP7P83rdfPXVl3z15X9YvuxrPKX+yWnofktq9+7fWfjvRRS7S1Bk0IVAkvALZtXsnpPD5XKhKEqN15RWQXO5XDzxxBMIIXjwwQdJTEzE4/EABK0MyXqy1a1bF6/XS25ublA0dlVh/R2GsBntS2NjYxkyZAhz5syhR48eTJ48mREjRvDrr7/i9XrN9eZJZQZJ/nUjCJAVLr6kI82bNWPt2rV4vDroAknzkZ+Xyy9r16AoYfy+aw+ZR7PQ0PxrR12wYcMG4hMSadOujd+HK/zxT6EHWShLSkpQFKVG570avUw1TaO0tJSpU6dy4MABJk2aRKNGjcxmWKqqEhYWFrR6UeNikJiYaFaGAEFbU1YFVvNXkiTCw8NxOp3mYykpKYwePZo5c+bQoEEDRo8ezSOPPMLGjRuRZRmHw2H2JzI85BW+Ax2/11QFBPUb1ufcFs3YsX0HRXluVCR0RwT79x+gIEflqqvSKDyyl//+dxuligNkKCnJZ+Pm3zinSWMaNWsCgEMRyLKEpDiCrymtrUBqGsbBM0zTOXPmsGzZMiZNmkSrVq3M9LVgayTrd9etWxfwD+qtrZTf59aKFJ/PR7t27XjhhRf417/+xeHDhxkzZgyvvPIK6enpZtd6I/Mp4HMRZZ5VABl0iIyKokPH9uRkZbF7+24Q4BM6W7bsxBEWw7AhN1M3Ppz1v67Dp8sgSRzNzGD9xv9yXssWpNZLRkcv+1z/N9iOnjPAuDJbPa1jxoyhe/fuIaOBrNkwRisORVHMusqT7cNaWzCG9EqSxDXXXMNbb73FnXfeydKlS7n99ttZtGgRbrfbnLli5USX1G5paUhC46slXyA5AKmU1T+vJz4xmisu70Pz885l7Zo1FBcVo0gq23f+Tn5BIb1690b1LyT93tyybwhqkXNeXl6NTxxQVZVNmzbxxBNPcMMNNzBo0KCAOsRQOeGNC0hERARJSUnmENmzSSit3fUkScLtdhMfH8/gwYN5++23ufLKK3n44YdZsGBBQEaQ5ROM3JxjOTu6xnnnnUvLFuexbu0a3C4Xhfk5rNu4ja7dupJcrz4dOrYj8/Ah9v9+ACSFH374P+ITkrgs7TJ8UCaQxwjqKLz8/Hzq1KkTrE04ZazzMIyDu2PHDsaPH0/v3r257777Arx4wcqWKY/VfHU6naSmppKenm6um2qDo+dksDaMliTJHL2o6zrnnHMOqamp1K9fnw4dOiDL8nHK16wpdJI/91VWiImJ5orul3H4wF52//EH/9uymcJCL5d16w66xAXtzkf3uNm0bhMFhcVs2f4757VoSZ3kBGQh/Bk+4lgGXlDPmIKCghollNYOcJIksX//fqZMmULDhg0ZPXo04eHh5hVWUZSQ6SljFUpVVWncuDHp6elmHefZoimPl5xuHMu9e/cyb948rr32Wtq3b18hhmkgC0uViGR0JZTo2OEiCvKOsu/AAX7771ac0Uk0PrclSHDeBc04JyWJ39atZfPmrRxKP8oll3TC4Y+F+G/CWE0GcU1pFDgnJSUFaxNOGasGzM7OZsaMGWRlZfHkk09St27dkFlH/hlGlUV2drYZqzxbNGV5DIHUdZ3FixejaRp///vfgT8PXxlpccdKsHRatzyf6Ihwfl2/gZ3b9pLauBnxCXUQWikpqUm0a30uWzev58effsLrg7S0bqYpLBmlXmXYQnkKGGldXq+XWbNmsXnzZh577DEaNGgQ7E07JZKSkswC87MZ43hu3ryZJUuWcOedd9K4ceOAtWdFwSwTR+nYZwCkpNSjT6/L+c/i/7Dq6x/o1LUTEREyCA+qCj0uu5QDe3/n/bkfUK9eKueefz66DrJht1qui0EVyry8vJA2X42DY5gyxt8LFixg+fLljB49ms6dOwOhs348GWJiYtA0rVaHRY6HdflhaMni4mIWLFjAOeecQ58+fczXHr/fjz8+6a8E8aPp/jpIZ0wMl/XqyX83bmLfviN069QRhwI6DnQiOa9NS+QwiW1b/8clF3ckKkwFn+aXcdm/NjVkPWiLHp/Ph8vlIikpKWSdDdZ1hbFWXLlyJW+++SZ33HGHOV+jphEXF4cQwkwgCNX9X9lYB9gaWvDHH39k06ZNjB8/nri4uL/4BLkso8ePBP6iZVQkReHitK48+thjRIRHcdH5zZB8OkIKQ/dKNGh+Lg8/8SC7/zjI36/pS4RDQaAhSSplcRR/CixBFEqXy4Wu68TFxYXsCWFdQ6qqyrp165g+fTr9+/dn8ODBNUYzlicmJgaHw2Gar6G6/ysbawWKJEkUFBQwb948WrZsyaWXXnoanweSJCNJAk3zkVo/lYkTH0VCLks80NEFSChER8dz2213oOsysqSW5blaxfsYQTurcnJycDqdREREBCVR+2QwTlZFUdizZw9PP/00559/Pvfddx9hYWE1toua0+kkNjaWo0ePnjVaEo51UDRM2KVLl5KRkcHgwYOJjIw8yXMwsKmOLCuIspYeiqqiqBKSItDRkRXJ/zwysuxAwokih+Gvyzzxfg+apszOzjZzQU+lhq4qsXrcjB1maJSJEycSFxfHgw8+SFxcXI0eRBQeHk5ycrIZqzyTKdE1CWNNqaoqR44cYc6cOfTv358LL7wwoA72Tz6BY+0/jh17WVbRhY4iSQihIQQ4HMfOa3OSXNnbjLDMic6hoAllbm4uTqcTh8MRMie31QlgVA4UFRUxbdo0Dh8+zKuvvkrjxo2Bmj2IKDIyknr16nHkyJGzSiit3Q0+//xzhBBcd911qKqKz+c7CU1p9OQp3/NHQpFkwF8reQzZfK3Zg8cS+zhRN4SgnVnZ2dk4nc6QcpQYVzXrGLp58+bxn//8h4kTJ9KqVasgb2HlIMsyKSkp5OTkmLHKswGfz0dYWBhbtmxh4cKF3H777aSmppotWk7tXCzXF9KMOsqW+8d5+iQImlAePXrUFMpQ0ZTWgleHw8FHH33ErFmzmDhxImlpaTUiOeBkqVOnDkVFRWdVrNJIRv/kk09o3Lgx/fr1C0i7O3nrp3y3OgOrYFq0pPnakzt/guroCQ8Px+FwhIyTx9gOh8PB999/b4Y++vfvX6sEEo4lEGRmZgZ7U6oU65JElmW++eYbVq9ezdChQ4mNjQ1IQfzrY2z1lopyj3HcxsqBT5y4kbOVoK0p8/PziYiIMFvUh8KkXmPhvX37diZNmkSPHj0YPnx4SF04KoukpCS8Xi9ZWVnB3pQqwdogy6jaKS4u5sMPP6RNmzZmCMR0wpzUuVde+xH49wk/4lhC3cl8T9A0ZUlJCbGxscH6+goYzp1Dhw7x6KOP0qhRIx544AGzY3dtFEojh7c2YixDjLCVJEl89913HDx4kGHDhhEVFRXw3Cl8crnbKW3VSb0qKEKpaRolJSVm3msoaElJknC5XEydOpXi4mKefvppU5sYz9cWE1YIQWRkJLGxsbVaUxrrRCEEmZmZvPjii/Tt25eOHTvi9XpD1oMelK3y+XwBQhksLWT9Xo/Hw4wZM9iyZQsvvvgiDRo0MIfQGISSp/hMkCT/TEijs11tx+Fw8Pnnn+Pz+bj++uvN9WWoWj/VIpTWRGA4JpTBTEa3dgf3+XzMmzePVatW8cADD9CqVStzHWIUxoaSl7gyUBSF1NRUcnJyao0FcDwUReF///sf8+fP595776Vx48YBzZhDkWrTlOXHmpWWlhIfH19dX18B44BomsaKFSt45513GDZsGP369avQBzRUD96ZIMsy9evXJzs728xmqW0Y2vDDDz8kISGB/v37B2SPndWaEgKr330+H263mzp16gTVdFUUhQ0bNvD0008zYMAAbrnlFsA/Daw2aw9jn9erVw+3211rY5WyLPPTTz/x7bffMmbMGGJjYwPylc/6NaVV25SWluLz+UhISKiurwcqDpTZvn07U6ZMoUuXLtx1111me0EjTBOqV9IzxbjgJCcno6oqhw4dCvIWVS6GleNyuXjvvfdo3749F198sakljd8fqgUF1SKU1jkPAHl5eUiSdAqZ+ZWDruumFjxy5AgvvPACTqeThx56yCwhU1UVRVFqdT6ocYGsU6cOkiRx5MgR4Ng4uppI+YJ0TdP4/vvv2b17N7feeqt5rhktQY/frS40CEryQFZWlpk4UF2hBiNmpaoqpaWlvPTSS2RkZPD888+bDYpr8xrSipEkUa9ePVRV5fDhw+ZzNdU6MM4jQ0tmZmYyc+ZM+vbtS5cuXczC5vLvCUWq1dFjkJWVRWxsrBliqI6dY2hBXdd55ZVXWL16NRMmTOCCCy5ACHHCNvW1EcMBEhUVRVRUFBkZGRVK1moa5at7vvzyS3Jzc7n55ptrXIy52kIiVrKzs4mKiqr2MIMkSSxYsICFCxcyfvx4unTpYq4da+rJeLoYYYGUlBQyMzMpLS2t0e0mrR7z7du389lnn3HXXXfRuHHjGlf7GhRHT25uLpGRkeawz6pIYzPMVZ/PZ14lV61axdtvv83w4cO55pprzDikoignaJRUezGOR2pqKkeOHKnxYREhBKqq4vF4+Oyzz4iJiWHgwIEB5Xg1RTCDstLNysoiMjLSTPSuqhFx1qZXmzdv5sUXXyQtLY2hQ4eaQhgKA3iCwbHWiP6sHqMxc00z9QyMbV+zZg0//vgjQ4YMMZ13NanTIFSj99VqQmRnZxMdHW2uKatqhxnetoMHD/Lkk09y7rnn8uCDDxIREXFWrSHLYz0WderUoaSkhIKCAvP5mnpxKioqYt68eTRr1oxevXoFe3NOm2pbU1rDIkVFRcTHxwcIY2ULppHfmZ2dzeOPP44sy4wfP57Y2NgArXA2Yl0uxMfHExUVRXp6OnBsrVkT+eabb9i7dy9Dhgyp0YOjqi0kYgidx+PB4/EQGRlpPmdcuc9EMK1drY1/i4uLmTlzJnv37mXGjBk0bdrUDIvUpDVGVWDso/j4eKKjo02hrCnWg/V4A2RkZDBnzhy6d+/OpZdeetwQSE2h2oTSMCWNbB6rUFaW1jI8qcZt7ty5LF26lBdeeIELL7wQqD2VHmeCoijmOj4hIYHIyMiAeZU1BcOZJ8syixcvpqioiBtuuAFVVc2+OzXxwlvtR6CkpASPxxMwvbkydpxVGBVFYenSpcyZM4dRo0bRvXt3PB5PjdECVY21F1FUVBQJCQlmW5CadBIbHtcdO3bw+eefc9NNN3H++ecHzKCsiQRFKL1eb6ULpdGNTFVVfvnlF1588UVuvvlmbrjhBvNqanMMoxzNqKvMysqipKSkxnhfjeNthEASExPp27dvlXrzq4tqP1Pdbjder9ccqW71BFq13V/t1PLDWgwNuW3bNiZNmkTXrl0ZMWKE2Ve2pl41qwLrvlBVlTp16pCZmUlhYWHIahjrgCXjJkkSv/zyC9988w0333wzKSkppm+iJl+Eqz331e124/P5iIiIAPwniMfjMYuJT6WRkVWgjdDHc889R1xcHKNHjza1cU0+QFWFNc83OTmZvLw83G43QMB4+FDB2nPH0JJut5uPP/6Ypk2bcvnll9ea41xtQmmcBKWlpaiqSnJycsBzp1p4an2dLMsUFRUxdepU0tPTmTVrFqmpqZW49bWbunXrUlxcTGFhYbA35YQYZrV1Hshvv/3Gxo0bmTZt2klMzKo5VGvyAPj7vbpcLnbt2kV6ejpCCHOmiKElT3ZNo2kamqbhdrt54403+N///sdTTz1FamrqWdX5+0xJSEgImMIValoSAi/CiqJQUFDApEmT6N27Nx07dqzRa8jyVKumFEKwb98+9u7dy6uvvso777yDw+GgadOmtG7dmi5dutCqVStTOK1JB9Z1pyHkxgyITz75hOXLlzNmzBi6du2K2+0OyRMrVImLiyM8PDzkOxBYe7guXrwYt9vN4MGDzRBPbTnm1b6mzMvLo379+owdO5aYmBj27dvH+vXr+fjjj/nggw/o0KED1113HR06dCA8PByfz2d2lTNMXGMtqSgKK1euNJPMDe+boXltTo7Y2FjCwsLMIbKhGng3LsR79+7l/fff55ZbbqF58+Yhu72nS7UIpVXruVwumjRpQlpaGnFxcXTt2pWbbrqJ/Px81q9fz6effspDDz1E9+7dGTx4MC1btjS1pbGWcDgcyLLML7/8wiuvvMK1117LkCFDQqrbek0iMjKS+Ph4srKyQtoMNI7t/PnziY6O5u9//3utE0ioxjWlLMvmSPV69eoRHh5urgklSSI+Pp4rr7ySqVOnMnHiRDIzMxk3bhwLFiwwB+7AscbNu3fv5vnnn+f888/n9ttvx+l0mhrU2hnb5q9RVZW6deuSkZFBaWlpSJ7khgW0YcMGVq5cyR133EG9evXMC35Nj01aqRZNaQhLSUkJubm5pKammj1wrIW1xrj1Pn360L59e2bPns0777xDZmYm//znPwkPD0eWZY4ePcqUKVNwOBw88MADJCUlmTmtteXAVCeqqpKSksLatWspKSnB6XQG3dIofxwlScLtdvPuu+9Sr149evfuHdBpoDZRbZrS2KmZmZkkJiYG1LkZhcaqqgaUFI0bN44xY8awaNEiXn75ZbxeL263m+nTp3PgwAEeffRRs7LcOsu+ptXPhQL16tXj6NGjuN3ukDnJrY2wADZu3MjmzZv55z//SWRkZECjs9oknNXq6CkuLiYzM/OEZTXWnWpo1/79+xMdHc0TTzxBYmIisizz/fff89xzz9G2bVsz0b22HJBgUa9ePYqLiykqKgr2plRACEFeXh7Tp0+nV69e9OzZs8JIidpEtaoTt9tNTk5OQIXIiTDGCQgh6NmzJ9dddx0TJkzgnXfeYdy4cXTr1i0gplkT8jVDmYSEBHNpEApYzVchBEuWLGH//v3ccssttXIKmpVqM1/Bn4zucrlwOp0n9T5DC+7bt4/ly5cjhGDw4MGm1806esDWlGdGTEyMOQowFDAET1VVDh48yMcff8wdd9zB+eefX+P7Cf0V1aopDc/eyVSFG50DsrKymDBhAl9//TX3338/I0aMCFg3qqpqFi3bnD4JCQmoqhoyU7iMY6xpGp999hmyLNO/f/+A19RWbVmtLSZLS0txOp0BZVsnQlEUSkpKeO2111i4cCFDhgxh7NixhIWF4fP5AjSjrSXPDKOuMiYmJmSEEvzhr40bN7Jy5UpuvfVWczxhTetOd6pUq3pxuVyEh4ef1JrS5/Mxd+5cpk+fztVXX82kSZPMAS21dYEfLIzQQkpKSkil2nm9Xj788EPq1q1Lnz59Ap6rrVoSqnlNmZ+fj6qqJ6UpV65cydNPP83555/Ps88+S6NGjYDQTJau6Rim4nnnnRcyjh4jY2vTpk0MHz6cuLi4AD9CbdWSUI3mqxCCrKwsZFk+7vAcIYS5gF+/fj3/+te/iIyM5JlnnqF169Zm3qMR17TXkJWLEMIUymB4sq0DfDVNIzs7m9dee41OnTrRo0cP0+lnHHtbKM8Q40pcVFSEw+E4rrYzsvz37dvH448/bvZqNTI3yn+eTeVijDAoLi4mPz8/KNvg9XrNbVmxYgVHjx5l8ODBFbrX1/ZOEtWqbgoLC4mMjDS7DpQnOzubl156iXXr1jF27FgGDBgQ0PrBpuoQQpCYmIjT6WTfvn1B+X5DE+7evZsFCxYwYMAAWrZsWcGxV9upVvO1uLiYqKio48YpNU1j1qxZfPLJJwwdOpS77rqL8PDwgJpKm6rBSMKIjIwkJiaGnTt3Vvs2GKV4mqaxePFiAK699lrTqjqbjn+1aUpN0/B6vcTExBAREYHP56O0tNSs5vj000+ZMWMGPXv2ZOzYsWZKXVhYWEBOrE3VIEkSERERxMbGmkJZndUXRtx506ZNLF++nBtvvJEmTZoE5LeeLVTbmtLr9VJQUEBMTAxOp9OsFpckiR9++IHJkyfTpk0bHnvsMVJTUwNyWmv7wj7YGPvW0JTWIbJQfVrKCIHUqVOHq6++ulq+MxSpNk3pdrvJy8sjKioKWZbRNI2IiAh27tzJI488gqIopqf1bDJVQgFjeSHLMvXq1SMnJyfA6VIdF0RJkli9ejXr1q1j2LBhJCYmVvl3hirVKpTGXErwH4SMjAyeeOIJDhw4wMSJE+nSpYuZhG5rxurDKnj169cnLy+P4uJigGorFi8sLOT11183QyBnc4FBtQllSUkJ+fn5ZhNmTdOYPn06S5cu5fHHH2fAgAHm1bq2VwGEGkbdIviFMj8/3+yWXlUXRyMmaQjfsmXL2L9/P0OGDDnri9WrVVOWlpaa2Txz585l5syZ3HvvvWZHMlmWcTgcZldzm+rBuq/r1q2Ly+Uye8AafVarAmMk4d69e3nvvfcYNGgQF1xwAXB2eVvLU21C6fF40HWd+vXr88UXX/DYY48xYMAAHnvsMZxO51l9EIKNtVOD0QPWOhqvqo5NeHg4kiSxbNkyhBAMGDDA7CBwNl+Uq63zgNGFLj09nenTp9OpUycmTZpEdHQ0Pp/PTpsLMobwRUdHk5KSwsGDB83nqiocIcsyW7Zs4eOPP+bOO++kYcOGdrII1agp8/PzcblczJ07F13Xee6552jSpAmAnRwQZKyDkiIjI0lNTTWLnSv7uFi7z/l8PmbPnk18fDx/+9vfTIE0eu6crVSbUGZnZ5Oenk5paSnTp0+nbdu2/g0oW0famjJ4WGPBUVFR1KtXzzRfK0tjGQJnIMsy//3vf1m9ejX33Xcf8fHxqKpqngu2pqwGjh49SkpKCk899RRpaWnV9bU2J4FVCIx5lbm5uZSWllbqvEprP96ioiKmTJlCly5duOKKK2xLyUK1CWV4eDjjxo3j+uuvt7ViiFFe6JKSksjJySE3N7dSnC6GwFlrIb/55ht+//13hg4detaHQMpTbY6ea6+9lqioKDO9ziZ0KD88KTY2ltzcXPLz80lJSTnji6i1a73D4eDgwYPmLJC2bdvak7bLUW1CWadOHfP+2byID0XKV/MnJCSYGVhQOQN/jEwtTdNYtGgRxcXF3HjjjYA91Lc89t6wqYDhdDH69VSGZWO0i9y2bRtLlizhxhtvpGHDhrbZehxsobSpQFxcHDExMRQUFACVo8kURcHn8/HRRx8RExNj1kraQlmR09zbOkJox8320HWBEGXPl3ODA+gC7BVlaBMXF0d8fPxftgU5mVpL43lFUdiwYQM//fQTQ4cOJTk52W6ifQJOa02paz40XUOWVTQNkCVkJHTdfwBkWYDwomkgoSIrZc2SJdAQ6EInTFawD0doEhMTQ0JCAkeOHDFDGOWzbIwkdqMHa3ltah0nYYxDf++997jooovo16+fuU61hbIip6UpzRkeQgBa2cQsBUkCRZERfmlEUco6Bzj8AunTy+r2ANtoCW1SUlI4evQoXq/XzEc1tJ5V+x1PqAwLyhoK+f7779m8eTNDhw49K9pEngmnpSllWUVBQpJlSoqL+XTeB3g8GkOHDvH335EkdM1/pfxi6Rfs3b+fgQP/QWpqCgKBLMn2YjbEadiwITt27CAnJ4f4+HgzI0eWZZxOp9lh7kQmrBFeUVWVw4cPM2fOHPr168eFF15oh0D+gtMSSl/ZgZCEICIinN937WDWrHdJTU3l2r9fi5AAXeOPPft49tnJNGrWnOuuvwFZBiEkhK4h5NozT7A2IoRgzZo1jBgxguLiYjweD06nk6SkJFJTU2nZsiUXXnghbdu2NWfDHK84XQjBf/7zH4qLixk0aJDt3DkJTk9Tqg4EOlJZ5ccdtw1j+VfLmDN7Nlf06k1UZBiyJLF86VIOHDrIQ/96jHNS6qIJkATIyEj2ijKkycrKYs+ePdx9992kpaUhSRKlpaUcOnSIrVu3snz5cubPn0/r1q0ZMGAAnTt3JjY2NmAtKUkSO3fu5KuvvmLgwIHmgF+7AOHPOS2hFICOhCIBQqP5eefTv19f5sz7mLXrN9CrRxqH9hzk008+oUvXLnRN64oG6BKoQkKSwJbJ0KZx48ZER0dzySWX0LVrV/NxY62Ym5vLzp07+fbbb5k6dSoNGjTgoYceomXLlqZXVZZlFixYgKIoFdpF2gkkJ+YMDXsJhI4kdG699Rac4U5mvTULV7GbZcuWcfhwOrcOuZXExEQCJgraF8mQp379+sTGxnLgwAHTsadpmtnCIz4+ns6dOzNujArxfAAACQVJREFU3DieeeYZYmJiuOeee/j888/N2tlff/2V7777jsGDB5OammquP+1ly59zyppSlN0sg+hAaLRo1Yoht97Kex98zLJly1i6bBkXd7qE7t16oAe+waYGkJKSQlxcHEeOHAECU/EM89Nw/HTs2JFWrVrx8ccfM336dLKysrj++ut56623aNeuHX379g2ISdqm659zykIpAYruXxsiyQhUdEASghtvvpbFX37Oiy9Oocjl4ZnJzxIXF4em6SgySJJ87ENsQprY2FhiY2M5dOiQKYRGF/PjhUeio6O56667SEpK4p133mHjxo3s2rWLF198MaCDofEeW1uemNMyX2UBSBICCSEpIDsQksS55zZnyE0D2PDrWi68uBNpZVpSFgIFCVkIJEDYBySkEUIQERFBQkICR48eNWd5WMu4rNO0jWbbuq5z7bXXctNNN/HZZ5/Rt29f2rdvX6FNpS2Qf85pCaUuC3QJdNnvvPE/KHA4wumWdhnJSYm0b9+euLgohACBP/XOn2Bnmy41AWOEQUZGBiUlJX/6WqM1KPgbpO3atYvzzjuPgQMHHndujM2fc3oZPZJAlwTGf5ruKzNjJByygyhnBA6HihAgy/7MHknGYrbaghnKSJKEw+EgMTHxpITSQFEUVq9ezfvvv88dd9xBixYtzKZotnY8eU5PKPGn1xnCpcgykiwDCrqQ0DWBLCsgGRkfhoYU2AIZ+hjmZuPGjSksLMTlcp3U+3Rd580336RVq1Zcd911gG2qng6nIZQCCR3J8i8YfUP99726D033mkKpW4VSsgqoTShiCFL79u2RZdn0wP7Z6xVFYe7cuaxdu5ZRo0aZU9Psqdunzuk5evA7eyTht0h1IRC6QAgJXUBCUhJhYWH4fDqyLAHlBNMWyJDG8K5ecMEFOJ1O9uzZ85evP3LkCDNnzqRHjx5cffXVdtjjDDitjB5JgN9po+DXnBK6EJS6Crnokov5+Zdf8CpONM2HR2iEq2VZPDY1AqODXZ06dXA4HGzduvVPXy+E4OOPP+bQoUNMnz7dztY5Q06zR4+EJGR/WMRIm1NUwiMiUWSJcIeErJW5zIWMJAvzfTahj5F5ExYWRkJCArt27QICRxhYy7e2bNnC+++/z+23307nzp3xer2EhYUFbftrOqchlBJIqv+fMi15TNb8LlYZiFCtj1X4BJsQxtrrtXHjxhw9epSSkhLCw8NNgTX+9Xg8zJs3D0mSGD58OA6Hw06nO0POPPf1OH/bh6LmYwhUw4YNKSgoMJtoWZMGwsLCWLt2LYsWLWL48OE0b97cngVSCdhuMZvjYghV3bp1KSwsNPv1WLsKFBUV8c4779C4cWMGDRpkPm+XZp0ZtlDanBBd10lOTsbn81UQSkmSWLFiBevWreP222+nXr16ZtK57eg5M2yhtDkuxpqyWbNmyLJMTk4OcKx/a3p6Oq+//jodO3Zk4MCBAKiqasYkbfP19LGF0ua4GOvG1NRUhBBmZztFUfB6vXz++efs37+fu+66yx76W8nYQmlzXAxNFxUVhaqq7N+/30w837FjBwsWLOAf//gHXbp0sR07lYwtlDYVMEIiRglXamoqhw8fRtd1SkpKmD9/PpqmMXz4cJxOpz2wqZKxhdKmAoYjR9M0wsPDad26NUVFRfh8PjZu3MiiRYu4+eabadq0qd0IqwqwhdLmuBiC6XA4aNu2LZmZmWRmZvLuu+9Sp04ds1bSjktWPrZQ2lSgfJeBxMREsrOzmTt3Lj///DMjRoygfv36eDwecyyBrSkrD1sobSpQfvJyQkICeXl5vPHGG1xyySX0798fVVXNLuk2lYstlDYVsPbeAb+mDAsLw+PxMHToUGJjY01N6nA4KmUEu80xqm2Ss03Nwipk0dHRJCcnc+2113LppZdWymRnmxNjC6XNXxIWFsbll1/OwIEDzUoRWyirDknYK3QbAutdy/fOdrvdZGdnk5SUhKr6r+OqqtomaxVhC+VZjwChgRBoOujICFlGMfq7IsrmkAoEclkTtLI1Z1kfXwBkW0ArC9sGsUHoOrqmIQEOVUGWJf84w2OvAKH5u9wrsn8UYpC29WzAFkob9P9v7/5do8rCMI5/z7l3/DmJiQiC2hghlqKpxG3dbQXtBEVE0TbW+jdYiNqvnfgDRN2t0qyNyC5GlBRikk7iJFssOHNn7jmvxbmZTLRR9gYHfT4QApk0gTy85973nPfEgMXA/MI8jx4/odVaXrd8dQTKXsGLF8+ZmZmhU3QGxp9pEFrdFErBkc5APnv2F1emp5mbmyODakJaxHkoi4/cvnmDa1ev0VpZSeNDnVMcN4BCKfjcQ+aJsaTotgmhZPUpMpXMgKOkaH+kU3ToBSNA+syBrqOol1oiUgUrxdA5BsaBrs3p9cQ0lbCqjusXrQpknVQppWKffTHwPQIljuqIllu9zVs2giql9PXfuH5xEVO6bsLZ2k/7n7io6YU1U6WUdJ9hrLbW5Z5uNErALANLVdJIofU+w6pHTaMkYphiWSuFUvrvaUIMRCIuz6tKuPbvYQZmOWaOzDkchhFJHct19xzK/6Tl68/OHDi/lj8zfBXJECKZh9SpbGBkNPLNNPJGmoyPx1n/FazURJVSqkpp7Nw5TtFu83p2lgzwzqfAktPpRFb+/Y9mc5SxkR0AeDIcXsvXmimUkq7/NcfByUma27bz59OntFrLNDyAB7eFv/95xcvZNxw+NMVIc2tqURqpUqojUistXwXvPRZKJvbv5+yZ01y/fovLFy/x6/HfGB3dwvzCW+7df8ievfs4dfJE2qxu1W4fNA29bjol8rMziCVgPVyjy4el9/x+5y4PH/zBwsIiIXQZHWty9NgvnD93gakjU2S5J8+rLqXlpFMj3/OP+LEolAIBYuxirsARgE0sLi7xbn6Rotdm1+5xJg5MMjYyTq9b4lzJps2pKYI1gEwnt2qkUAoWwWIAuuACxAzf2Lrud0qLECFGw7tIllvaG0sGliuUNVIoZcDqXp2vaXPodu6Nohc9MuBbeo4K40bR47nIkFEoRYaMQikyZBRKkSGjUIoMGYVSZMgolCJDRqEUGTKfAHElAExffuO2AAAAAElFTkSuQmCC)
Prove that UZ = YZ
![](data:image/png;base64,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)
Maths-General
Maths-
In the given picture,
is an isosceles triangle with
and AD bisects the exterior angle A. Prove that
![AD parallel to BC.](data:image/png;base64,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)
![](data:image/png;base64,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)
In the given picture,
is an isosceles triangle with
and AD bisects the exterior angle A. Prove that
![AD parallel to BC.](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that the sum of squares of sides of a rhombus is equal to twice the sum of the squares of its diagonals.
Prove that the sum of squares of sides of a rhombus is equal to twice the sum of the squares of its diagonals.
Maths-General
Maths-
In the given figure
, and
. find ![straight angle B C D](data:image/png;base64,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)
![](data:image/png;base64,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)
In the given figure
, and
. find ![straight angle B C D](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Find the value of x y and z from the given figure.
![](data:image/png;base64,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)
Find the value of x y and z from the given figure.
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that ∠YXZ ≅ ∠UWZ
![](data:image/png;base64,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)
Prove that ∠YXZ ≅ ∠UWZ
![](data:image/png;base64,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)
Maths-General
Maths-
Find x: if [9/5]−5 × [9/5]12 = [9/5]3x−2
Find x: if [9/5]−5 × [9/5]12 = [9/5]3x−2
Maths-General
Maths-
Find
in the below figure.
![](data:image/png;base64,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)
Find
in the below figure.
![](data:image/png;base64,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)
Maths-General
Maths-
Use the given information to prove that the given triangles are congruent.
![](data:image/png;base64,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)
Use the given information to prove that the given triangles are congruent.
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that the sum of the squares of the diagonals of a parallelogram is equal to sum of the squares of its sides.
Prove that the sum of the squares of the diagonals of a parallelogram is equal to sum of the squares of its sides.
Maths-General
Maths-
Find the value of m for which 5m / 5-3 = 55.
Find the value of m for which 5m / 5-3 = 55.
Maths-General
Maths-
In the figure, the sides AB and AC of
are produced to P and Q respectively. The bisectors of
and
intersect at O. Prove that
.
![](data:image/png;base64,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)
In the figure, the sides AB and AC of
are produced to P and Q respectively. The bisectors of
and
intersect at O. Prove that
.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQQAAADVCAYAAACxHY40AAAgAElEQVR4nO3dZ1iUZ9738e8MHSlSpSNdsFDsMbGtBhugWCL2gsYWXXdTN5tNcuz96O4mWU0xsaBGxAJ2sQYbICoaRZSyiBJpioAgShWY63mxK/edjRow4BTOz3HkTRzn+ovjb85+yiRJkhAEQQDkyi5AEATVIQJBEIQmIhAEQWgiAkEQhCYiEARBaCICQRCEJiIQBEFoIgJBEIQmIhAEQWgiAkEQhCYiEARBaCICQRCEJiIQBEFoIgJBAykUChoaGpRdhqCGRCBoGIVCwenTp9m+fTuNjY3KLkdQMyIQNEx8fDynTp0iJyeHqKgoEQpCi4hA0DBZWVk8fPgQc3NzkpKSEOffCC0hAkEDGRsbY2BggJ6eHjU1NcouR1AjIhA0yIkTJ/jXv/7F7373O3r37o2xsTH79u1DoVAouzRBTWgruwCh9dy5c4e4uDiKiorQ09Pj+vXraGtri26D0GwiEDSEJEnU1tbSq1cvJkyYgIGBAcePH0cul1NRUYG5ubmySxTUgEycuqwZjh49yqFDh1i8eDE+Pj4AFBUVsXbtWpydnZk9e7aSKxTUgRhD0BBlZWXIZDJcXFya/p+NjQ2mpqaUlZUpsTJBnYgWgoYoLy+nqqoKOzs75PL/zfmSkhIArKyslFWaoEZEIAiC0ER0GQRBaCICQcNIkkRdXR21tbXKLkVQQ2LaUcMUFBRw9OhR9PX1mThxIgYGBsouSVAjIhA0SG1tLcePH+fLL7/EyMgImUxGSEgIJiYmyi5NUBOiy6AhFAoFZ86cYe/evZibm6Onp0dERASJiYk8fvxY2eUJakIEggaQJInU1FQiIiLQ19fn73//Ox999BGPHz9mx44dZGdnK7tEQU2IQNAAd+/eZcOGDeTk5DBz5kz69u3L8OHDef/99ykqKiIyMpI7d+4ou0xBDYgxBDX36NEjDh8+zLlz5wgNDWXo0KFoaWkB8Oqrr3Lr1i327NmDnp4eb731lligJDyXCAQ1plAouHjxIrt376Znz57MmDEDY2Pjpl+3sLDgjTfe4MGDB8THx2Nvb8+UKVN+9hpB+L9El0GN3b59m+joaBQKBTNmzMDZ2fkXr7G3t2f69Ol069aNvXv3Eh8fT11dnRKqFdSBCAQ19eDBA7Zv386VK1eYPHkyr7zyCjKZ7KmvdXd3Z+bMmZiZmREREUFSUpKYeRCeSgSCGqqpqWHPnj3ExsYyevRoJkyYgI6OzjNfL5PJCAgIYN68edTW1hIZGSlmHoSnEoGgZhQKBVevXmX//v10796dsLAwTE1Nf/X3aWtrM3DgQObMmUNubi4RERHk5ua+hIoFdSICQc0UFRU1nZM4bdo0PDw8mv17dXR0GDZsGIMHDyY+Pp7NmzdTWlrahtUK6kYEghopLS0lKiqKc+fOMWbMGPr06dM0xdhc5ubmTJ06lSFDhnD69GkOHTrEo0eP2qhiQd2IQFAT9fX1nD59mujoaLp3786oUaNeeOOSu7s74eHhdOvWjU2bNnHu3Dnq6+tbuWJBHYlAUAOSJHH58mWio6NxcXFh7ty5ODo6PnNWoTm6dOnC3LlzMTQ05KuvviItLa0VKxbUlQgENVBcXExMTAzV1dXMnTsXPz+/nx2T9iJkMhk9evTgvffeo7i4mLVr15KTk9NKFQvqSgSCiquqquLAgQNcuXKFUaNGMXDgQLS1W2eBqba2NkOGDGHevHmkp6cTGRnJgwcPWuW9BfUkli6rsNraWuLj44mMjKRr166MGjWKDh06tPpzJk+eTHFxMUePHsXCwoLZs2djZGTU6s8RVJ8IBBV2584d1q9fD8DUqVNxcnJqk+eYmJgwZcoUHj58yObNmzExMWHcuHHiYJV2SHQZVFRpaSmbN28mOzubxYsX06dPn1brKjyNi4sLM2fOxM7OjjVr1pCQkCD2PLRDIhBUUF1dHbGxsSQlJREWFsbo0aPR19dv02fKZDK8vLz48MMPMTExISIigoyMjDZ9pqB6RCCoGEmS+PHHH9mzZw8eHh5MmzbtpTXdtbW16d+/P2+++Sb5+fmsW7eOgoKCl/JsQTWIQFAhkiRRVlbGl19+SX19PZMnT37qlua2NmLEiKaZh/Xr11NcXPzSaxCUQwSCCikrK+Mf//gHV65cYe7cuc/d0tyWjI2NCQ0NZfTo0Rw7doy9e/dSUVHx0usQXj4xy6AiqqurOXLkCIcOHWLMmDG89tpr6OnpKa0ea2trxo8fT0FBAdHR0VhaWjJixAgxHanhRAtBRVy+fJk9e/bg7e3N3Llzsba2VnZJuLq68uabb2Jubs6WLVs4d+4cDQ0Nyi5LaEMiEFRAcXExERERlJeXs3TpUrp3797iXYxtQUtLi+7du/PHP/4RbW1tYmJiuHnzprLLEtqQCAQle3KCUWZmJuPGjaNPnz7KLukXevXqxaRJk0hPT2fFihXiYBUNJgJBiWpqaoiNjSU2NpYhQ4YQHBzc5usNXoSuri4jRoxg5syZ3Lhxgw0bNlBUVKTssoQ2IAYVlUShUJCamsq6deuwt7cnLCwMFxcXZZf1TGZmZowePZo7d+6QmJiIs7MzkyZNatbxbYL6EC0EJbl37x579+7l7t27hIWF0aNHD6VMMbaEg4MDM2bMwMfHh5iYGOLj46mpqVF2WUIrEoGgBFVVVezcuZNTp06xaNEihg4d+pvPN3gZZDIZ7u7uLF68GJlMxooVKzh37pyyyxJakep/CjXQ8ePH2bNnDwEBAW22pbkt+fj48N577yGXy4mMjBQHq2gQEQgvkSRJ3Lx5k+3bt2NkZMS0adPo3Lmzsst6If3792f+/PkUFBQQEREh9jxoCBEIL1FxcTHr1q0jLy+PWbNm8dprr6n8uMGzGBoaMmrUKAIDA0lKSmLHjh3iSHcNIGYZXpKamhqOHTvG2bNnmTBhAoGBgWobBk9YW1szdepUHjx4wK5du+jYsSNhYWFiebMaEy2El+Tq1ascPHiQgIAAxo0bh5mZmbJLahX29vbMnTsXf39/oqOjSU5OVnZJwm8gAuElyMzM5Pvvv6empoYJEybg5uam7JJalZubG3PmzKFDhw5s3LiRy5cvK7sk4QWJQGhjRUVFREZGkpyczPDhw+nZs6daTDG2lL+/P9OmTaOoqIhvv/2W27dvK7sk4QVo3idThdTW1nLkyBESEhIYPnw4EydO1NiDS3V1dQkODmbGjBncuHGDtWvXcufOHWWXJbSQGFRsQ+np6Rw+fBhPT09mzZqFg4ODsktqU3p6eowcOZKioiJ2796NsbExs2fPxs7OTtmlCc0kWghtpLCwkKioKGpra5kyZQpdu3ZVdkkvRadOnZg8eTL9+/dn27ZtHDx4kMrKSmWXJTSTCIQ2UFZWxvbt20lOTmb06NEquaW5LXXu3JlFixbRq1cvDh06xMWLF5VdktBMIhDawPnz59mxYwfdu3cnODi4Xe4I9Pb2ZvHixWhraxMRESFmHtSECIRWlp6eztatWzE2NmbevHnY29sruySl6d69O1OmTGmaebhx44aySxJ+hQiEVlRSUsL3339PQUEBb7/9Nr169VL71Yi/haGhIWPGjGH69OncuHGDzZs3i4NVVJwIhFZSX1/PwYMHuXjxIiEhIQwfPlzZJakEQ0NDgoKCGD16NImJicTGxopBRhUmph1bSWJiIuvXr8ff358JEyao5FFoymJpacnkyZObFmnp6ekRGhoq9jyoINFCaAXp6emsWrUKPT095s+fr9JHoSlL586dmT9/Pqampnz//fdikFFFiUD4je7evcvWrVvJz8/nj3/8I35+fsouSWX5+PiwfPlyFAoFX3zxBT/++KOySxL+iwiE36Curo4TJ06QkJDAuHHjGDZsmEbuU2hNAwYMYObMmU0DsOJId9UiPr2/QUpKCgcPHsTb25uZM2eq3VFoyqCvr09QUBBTpkwhKyuLyMhI7t69q+yyhP8Qg4ovKC0tjdWrV/Pw4UPCw8PV9ig0ZbC0tGT8+PE8evSI2NhYbGxsxJHuKkK0EF5ASUkJu3fvJjs7m+DgYAYMGKDsktSOnZ0d06ZNo1u3bkRERJCUlIQkScouq90TgdBCNTU1xMXFcfLkScaMGSOmz34DR0dH3nvvPSwtLVm3bp3Y86ACRCC0UHp6Onv37m0aN7C1tVV2SWrryT0Py5cvp76+nnXr1pGdna3ssto1EQgtcPPmTbZu3UpFRQUTJ07EyclJ2SVphFdeeYVJkyaRn5/fdNqS6D4ohwiEZrp37x4xMTEkJyfz+uuv06dPH7S1xZhsa3iy52HYsGH88MMPbNmyRZy2pCQiEJqhrq6OY8eOsWfPHrp37y5GxNuApaUlYWFhvPbaa0RHR3P48GEePXqk7LLaHREIzZCdnc327duxsbHh97//Pc7OzsouSSM5Ojry17/+lZ49e7Ju3ToSExOVXVK7IwLhVxQVFREVFQXAvHnz8PDwUHJFmksmk2FlZcXChQvp1KkT3333HZcuXVJ2We2KCITnqKys5ODBgyQmJjJy5EgGDhyIrq6ussvSeL1792bhwoU0NjayZs0asrKyUCgUyi6rXRCB8AySJJGcnMzatWtxdnZm7NixmJubK7usdkFHR4ehQ4cSFhbWdAKVWN78cohh8mdIS0tj1apVSJJEeHi4xh+hrmo6dOhAUFAQd+7cYcuWLVhZWTF9+nQRym1MBMJTlJaWsmXLFioqKnjrrbfo27evmGJUgo4dOzJnzhwKCwuJjIzExMSEKVOmoKenp+zSNJboMvwXhULBDz/8wOXLlwkMDCQ4OFjsYlQiKysrFi9ejIuLCzExMcTHx9PY2KjssjSWCIT/Q6FQkJaWRlRUFB4eHkyePBlLS0tll9XueXh4MH/+fOrr6/nss8+4dOmSCIU2IgLh//jpp59YtWoVDx48YNKkSWK9gYqQy+W8+uqrzJ49m8rKStatW8etW7fE8uY2IALhP6qqqti9ezdpaWnMnz+fPn36oKOjo+yyhP8wNDRk5MiRzJkzh9zcXHbs2CFmHtqAGCn7j5MnTxIbG8uoUaMICQnR2Fua1Zm5uTmhoaE8ePCA/fv3Y2Fhwdy5czEwMFB2aRpDtBCAixcvEhERgbW1NdOnT8fMzEzZJQnPYGFhwdSpU/H19WXbtm3ExcWJ8YRW1K4DQZIkiouLiYiIoLKykvDwcNzd3ZVdlvAr7OzsWLRoEba2tqxfv57k5GQRCq2kXQdCbW0t27Zt49KlS4wdO5ZXXnlF2SUJzeTt7c2CBQvQ0tJi/fr1XL9+XSxvbgXtNhAaGxs5efIkGzZsYPDgwUyYMIGOHTsquyyhmbS0tBgwYABTpkzh7t27TactiZmH36bdBkJKSgpbt27F09OT8PBw7OzslF2S0EIdOnQgMDCQMWPGkJiYSGRkJPfu3VN2WWqtXQZCUVERu3fvpqKigvnz5+Pp6anskoQX1LFjR0JDQxkxYgQJCQmcOHGCx48fK7sstaXy046SJNHY2PizpqBMJnvhvQWNjY1ER0cTHx/PhAkTeO2118R6AzVnb2/PokWLqKio4Pvvv8fY2JiQkBBll6WWVD4QSkpK+Oyzz7h9+zYymQyFQoGPjw/vvPMOxsbGLXqvxsZGDh48yMaNG/H19SU4OLjF7yGoJldXV958800+++wz1qxZg42NDX379lV2WWpH5bsMjx494sqVKwQEBDB27FjGjRuHmZkZ3333HZWVlS16r9TUVDZv3oyNjQ0zZswQtzRrmICAAObNm4eOjg7ffPMNN27cEIOMLaTygQBgZmbGuHHjmDJlClOnTqVXr15cvnyZ2traZr9HUVER+/bt48GDB8yYMYNXXnlFbGnWMHK5nP79+zN58mRu3rzJ+vXryc/PV3ZZakUt/kVIkkRlZSU1NTXAv/cdyGQyZDJZs35/Q0MDZ86c4fz584SEhBAUFCS2NGuoDh06EBISwt27d9myZQtmZmbMmzcPa2vrF3o/hUJBXV0dCoUCuVyOvr5+sz936kjlA0Eul1NYWMjSpUub1gkUFxdjbW3d7L+Y8+fPExkZiY2NDePGjRNHqGs4ExMTFi5cSFVVFceOHcPNzY3Jkye/0HsVFRXx5z//mdzcXLp27coHH3yg0bd1qXwgSJKEmZkZISEhTX3+lJQULl269Kv9Q0mSSEtLY+PGjdTU1DBp0iQcHR1fRtmCkhkbGzNjxgzy8vJYs2YNenp6hISEIJc3r5csSRLZ2dlEREQwbNgwLC0tuXv3Lt999x3Tp0/Hzc2t2e+lTlT+TyRJEkZGRgwdOpTAwEACAwN59dVX0dbW/tVAKCkpISoqitTUVEJCQhgyZIiYYmxHnJ2dCQsLw9jYmIiICBITE5u956GwsJCNGzfSt29fJk6cyOuvv05oaCj+/v4cOHCAioqKNq5eOVS+hQD/vjnp9u3b6OvrA//+h25ubo6WltYzf09jYyOJiYmcPHmSoUOHMm3aNDHF2M5oa2vz2muv8fDhQ9auXUtkZCSWlpb4+Pj8anezsrKSnJwcpk+f3vQlYmxsTGBgILdv38bQ0PBl/BFeOpUPBB0dHRobG/nss88wNDREkiQcHR2ZP3/+M88skCSJ1NRUYmJi8PHxYfbs2eIotHbKwMCAUaNGUVlZyaZNm4iJiWH+/PnY2dk9NxRkMhlyufwXrzE0NMTHx6ety1YalQ8EGxsbPv/886Z7/iRJwtTUFC8vr2f+hebn57NlyxaKi4t599136dKly8ssWVAxhoaGhIaGUlZWRlRUFFpaWixYsOC5Mw9PWyEL8PjxY4qKirC1tdXI7qfKB4Kuri7e3t7Nfn11dTX79u3jxIkThIeHN403CO2biYkJU6dOJScnh8OHD+Ph4cHEiROf+dnQ19fH1taW/Px8unXrBvy765qQkEBKSgrh4eEaeUeE1ieffPKJsotoLY2NjcTGxrJhwwZ69+7NO++8I6YYhSZGRkY4ODiQlZVFSkoKVlZWODk5PXUsytjYGBsbGw4dOoRCoaCyspIrV65w/vx5xowZg7Ozs0bOMmjUV2daWhoxMTFYWFgwc+ZMcb6B8As9evRg1qxZfPfdd2zduhUzMzMCAgJ+8Y9bS0sLPz8/ZDIZ69evp6SkBCcnJ2bNmoWvr6+Sqm97MklDFnsXFxezYsUKfvjhB8aNG0doaGibdBXkcnlTv1ImkyFJklgv3wqerDxt61OP5HI51dXVHD9+nD179uDv78/ixYvx9fV96kW+kiSRn59PXV0dhoaG2NjYPHd2S91pRCA0NDSwbds2FixYgKGhIe7u7m1y3ZdCoaChoaFpBLqhoQG5XK6Rg0svW319PZIkoaOj0+ZLg2UyGbW1tdy6dYtHjx4xbtw4PvnkEzH4jAZ0GRobG7l8+TLbtm2jtrYWe3t7fHx8MDQ0bNVvGy0tLYqLi0lKSqJDhw64u7vz448/YmlpSf/+/dHT0xMthRcgk8mor68nKSmJ+/fvM2TIECwsLNq0pSCXy6msrOT+/fuUl5fzww8/8Oqrr+Lo6Nju97iofSDk5+ezY8cO8vPz8fX1xcjIiGHDhvG73/2uVb+5dXR0uH79OmVlZVhZWRESEkJ5eTndunXjww8/xNTUVBzy+QLkcjlVVVV8+umnZGZmsmzZMnx8fGhoaGiT58lkMqqrqzl58iS3bt3Cw8ODmpoa9u7di6OjI0FBQRo5WNhcah0I1dXV7N27l1OnTrF8+XJ8fX1ZsWIFW7duxcbGhiFDhrTqX66xsTFaWlp06tQJCwsL9PX1MTQ0xMrKqt1/s/wWBgYGdOrUiezsbExMTNp0ZqixsZELFy6wY8cOrK2t+fDDD5HJZPzjH/9g27ZtODg44O/v325DQW3/1JIkcezYMbZs2UL//v2ZO3cuffv25f3330eSJD766CNOnz5NfX19qz2zpqaGR48e4eDggEKhoL6+HiMjI9FV+I20tbWxt7entraW6urqNnvO48eP+eGHH1i5ciUymYwPPviAnj174ufnR1hYGIWFhXz++efcvn27zWpQdWoZCJIk8eOPPxIZGYmrqyvTpk1rSvR+/frxl7/8BXNzc1auXMmpU6dadJDK81RUVCCXy+nYsSM1NTXU1tbi4OAgBhV/I5lMhqmpKTo6Oty/f79NnlFXV0dcXBxffPEF1tbWfPzxx/Tu3Rv4d7dl6NChvPHGG8THx7N161ZKS0vbpA5Vp5aBUFJSwp49eygvL2fq1Kn06dOnaWRaJpPRv39//vSnP2FsbMyaNWs4f/78b35mZWUlGRkZ6Ojo4Onp2RQymn5gxsugpaWFvb09enp6pKSkNC1Tby1lZWUcOHCANWvW0LFjR/74xz/Sr1+/n73G2NiYyZMnExISwsGDBzl9+nSrfZGoE7ULhOrqauLi4khMTCQoKIgRI0b8YopRLpfzyiuvsGzZMu7du9d0icdvUVZWRnp6OkZGRlhYWJCXl4euri7W1tYaPS/9slhYWKCtrU1mZiZVVVWt9r7l5eXs3r2bb775BhMTE959991n3tBlaWnJO++8g4uLC1FRUSQnJ7e77qBaBUJ9fT3nzp0jKioKT09PQkNDnzuY16tXL+bMmUN2djaff/45OTk5L/zs/Px8cnJy6Ny5Mw0NDWRnZ2NkZISrq6sIhFZga2uLk5MTN2/ebLUWQkVFBXv27GHbtm24u7vz6aef0qdPn2e+Xi6X4+rqytKlS3n8+DFbtmzh1q1brVKLulCrQEhLSyMyMhIDAwPmzZuHk5PTc5vrRkZGvPHGGyxcuJCMjAxWrlzJjRs3WvzcqqoqfvzxR6qrqwkICEChUJCfn4+lpSVWVla/5Y8k/IeBgQF+fn7k5+eTkpLym5vrDx48ICYmhp07d9KjRw/efvttvLy8mvV7+/fvz/Tp08nNzSUqKkpjD0N5GrUJhNLSUnbu3ElGRgaTJk2iV69ezVqa3LFjRyZMmMDs2bPJzs7mn//8J1lZWS16dllZGefOncPR0RE/Pz+Ki4spLy/Hw8OjTVZEtkf6+vr4+/vToUMHzp49S3l5+Qu/V1lZGTt27CAqKgofHx/efPPNFp1hoKOjQ2BgIMOGDePAgQNs376dhw8fvnA96kQtAqGmpoaDBw9y9uxZhg0bxogRI5667vxZOnbsyPjx45k5cyapqamsXr262aHQ0NDA1atXycvLY+DAgVhZWXH16lUkScLf37/pFCfht5HL5Xh5eeHv78/ly5dfeJT//v377Nq1i6ioqKYbop9sX24Jc3NzQkJC6NKlC5s3byY+Pp66uroXqkmdqHwg1NXVkZSUxM6dO3Fzc2PWrFkvtIvR1NSU8ePHM336dJKTk5sdCmVlZZw4cQILCwv69+9PTU0NV69exdHRke7du4spx1ZkaGhIcHAwpaWlJCcnt3hNQnl5Ofv27SM6Ohpvb2+WL1/+wqcbyWQyPDw8WLp0KXZ2duzatYv09PQXei91otKB0NjYSFZWFmvWrCE3N5ehQ4fi5OT0wu+nr6+PlZUVDQ0NxMTE8M9//vO5A41VVVXExcWRkpLS9Ozs7Gzu3LlDv379sLGxeeFahF/S1dVl8ODB+Pv7c+TIkRYtECovLyc6OpqdO3fStWtX3nvvvWaPGTyLjo4OvXv3Jjw8nLy8PLZs2dJm6yRUhUofkFJeXk5ERATR0dE8fPgQLS0tzMzMcHBwaPHW5szMTDZv3symTZtwcXFh4MCBXL9+nXv37tGtW7dfHMAqSRJXrlzhq6++wtramgULFiBJEuvXr6eoqIjFixfj6Ogo1iC0IplMhpGREfX19Zw4cQJTU1N8fX1/dRanrKyM7du3s337dnx9fVm0aNFvDoMn5HI5jo6OTd3WhoYG/P39NbZlqLKBUFlZyd69e4mOjiYwMJDhw4dz5coVzp49y/Xr16moqMDQ0BADAwMkSaKhoYHGxsam/xoaGigrK+PKlSvs2LGD77//nrS0NLp27cqcOXOwtbXl7NmzJCUloVAocHV1/dka+uvXr/Ptt99y9+5dli5diq+vL0lJSezatYtBgwYxbtw4MX7QBmQyGRYWFmRnZ/Pjjz/i5ub23Ls0SktLiYmJISYmBj8/PxYsWNCiI/eaQ0dHBycnJ0pKSjh+/Dimpqa4ublpZCio5OamhoYGEhMTiYqKorCwkNDQUMaPH4+Pjw+nTp0iMTGRy5cv4+3tjYuLC1paWr9YQFJVVcW9e/e4d+8ehYWFODs7M3PmTHr16sWdO3eIjY3FxMSEAQMGcOrUKbS0tJgxYwbOzs6Ul5ezc+dOUlJSmD9/PkOHDuXevXscOnQIXV1dxo4di5GRkZJ+OprPzs6O0NBQPv30U7Zs2YKLi8tTb0sqKSlh//797N27l+7du7No0aI2O9PA1taWCRMmkJmZyZYtW7CxsWHAgAEtGtxWByoXCJIkkZWVRWRkJNra2gwePJjY2FiysrIYM2YMS5YsYezYsdy6dYtr165x8eJFSktLf7H1WFtbm06dOtGnTx98fHxwdXWlvLycyMhILly4gLW1NeHh4fj6+hIdHc3x48epr68nPDycXbt2ceLECYKCgpg8eTIymYy4uDgyMzMJCgqiR48eoqvQxvr06cP48ePZtGkT0dHRzJw5EzMzs6ZfLysrY/fu3cTExNC9e3eWLFmCp6dnm9VTX19PWVkZ9+7dIzMzk02bNmFjY9PqrRFlU7lAqKurY9u2bZSUlLBkyRK6du3KsWPHOHz4MP/v//0/HBwc8PX1ZfDgwfzud7+jsrKSqqqqX7QQ9PX1MTU1pbKykgsXLrBv3z6ysrKQyWSEhoYyevRo3N3dmxY5aWlpsXv3bk6cOMG9e/eYPn06c+bMoWPHjuTk5LBt2zY6duzI2LFjxVbnl8DExITx48dTWFjIjh07mtaTGBkZ8eDBA7Zv38769etxd3dn0aJFbRoGDQ0NJCQksHr1arS0tJg6dSpXr15l3759ODk5adTnQTbQNh4AABX1SURBVKUCobKykl27dhEXF8fkyZMZOHAg5ubmdOrUiVdeeYUzZ85w8uRJdu/eTUJCAubm5hgaGmJpafnU/euVlZUUFBSQn5+PhYUFr7/+Oq+++ir9+/f/2dSltbU106dPR5Ikvvzyy6ar45ycnLh37x5fffUVNTU1LF++HFdX15f5I2nX7OzsmDt3LkVFRezYsQNDQ0MGDBjAoUOH2LRpE7m5uRgbG5OVlYWTk1Or36YkSRKlpaVs3bqVI0eO0KFDB/7617/i5ubGpk2biIuLw8HBgUmTJmnMeJLKDCo2NDQQHx/PV199hYuLC3PmzGlamqynp4etrS3e3t706tULf39/LCwsKC4uJjc3l/v371NcXNw0ZnDv3j2KiopoaGigW7dujB07lrCwMAIDA+nevftTPzgmJiZ07twZAwMDcnJyMDc3x9TUlAMHDnD06NGmnXCaeoWXKpLL5Zibm2NnZ0dGRgbnzp3jX//6F2fOnCEgIIDQ0FBKS0tJTEykrKwMc3NzOnTogLa29m/q0ikUCh48eMDly5dZt24dx44dw93dnQULFjBo0CDMzc2bBj4vXbqEra0tjo6OGrGnRWUOWS0qKuLdd98lJSWF1atXM3jw4Of+gKuqqigpKaGiogKFQvHUXWlPTuIxMzNr9gektLSU1atXk5CQQOfOncnMzKRfv368++674uZoJZEkiePHj/Pxxx9TVFTEmDFj+MMf/oCjoyPJycls27aNK1euYG9vz5gxYxg8eDD29vZoaWk1eyZAkiTq6+tpaGjgX//6F9u2bSMpKYnS0lLmz5/PuHHjfnbjsyRJJCYm8vnnn2NiYsJHH33UalOdSiWpgLq6Oukvf/mL1KVLF2nbtm3KLkcqKCiQFi5cKDk6Okq9e/eWkpOTlV1Su/bo0SPpm2++kfz8/KR58+ZJN2/ebPq1xsZGqbi4WNq/f780evRoyd3dXRo4cKC0bNkyKSYmRsrOzpYePXokVVVVPfO/iooKKTU1VdqwYYM0Z84cyd/fX3J2dpZmzZolxcfHS1VVVU+tq76+XtqzZ4/k6+srLVu2TKqsrHxZP5I2o/QxhMbGRvbu3cuZM2cYP348I0aMUHZJ2Nvbs3TpUnR0dDh9+jTnz5/Hzc0NCwsLZZfW7pSXl7Njxw727NnDkCFDWLBgAW5ubk2/LpfLsbKyYuTIkXTr1o2UlBROnz7N5cuXOXfuHIaGhnTs2PGZ08SSJPHgwQMePXpEY2MjHTp0YOTIkQwZMgQfHx9sbGyeeb7ik9ulx44dy86dO5suIVbnW8aVGggKhYLMzEy2b9+Ou7s7kyZNUpn78ry8vHjzzTeRyWTs378ffX19xo0b99wLQoXWde/ePfbv38+uXbsICAhg7ty5eHh4PPW1urq6uLm54eDgQN++fcnJySE9PZ07d+5QUFBAWVnZM7uNTk5OODg44Ofnh5OTE9bW1lhaWjZrTMDCwoIJEyaQk5NDbGwsrq6uBAUFqe19okodQ7h79y5ffPEFFy9e5E9/+hPDhw9XqYEZSZK4efMmX331FampqUydOpWwsLBnXkMvtJ4nx+RFRkYSEBDAkiVLnnvj93+TJIna2lpqamqorKx87vkKRkZGdOjQASMjoxf6/CkUCs6ePcvf/vY3TE1N+eCDD+jRo0eL30clKKuvUl5eLq1YsUJyd3eXPvvsM6msrExZpfyq9PR0KSQkRHr11Vel/fv3SzU1NcouSaNVVFRI3377rTRo0CBp3rx5UnZ2trJLapY9e/ZIffv2lZYsWSI9fPhQ2eW8EKVMOzY0NLB//35iYmIYMGAAc+fOferSVFVhaWmJu7s7GRkZnDx5ElNTU1xcXDRyLbuyVVRUEBkZ2XTv4vLly3F3d1d2Wc3i6uqKQqHgwIED1NXV0bNnT7XrOiglEK5fv87GjRsxNDTkrbfeeuE96y+LTCbDzs4OZ2dn0tLSOHPmDJaWljg5OYlQaEUlJSXs2LGDbdu20adPH+bPn9+mKxBbm7a2Nra2thQXF3PixAk6deqEm5ubSnWDf81LD4TS0lI2bNhAXl4es2bNYtCgQWqxL0Amk2Fra0vnzp1JTU1tWinp6OiocRtclCEvL489e/YQFRVFnz59WLBgQYvGDFSFsbExlpaWXL58mStXruDq6oqtra3a3AT1UgOhoqKC6Oho9u/fz/Dhwxk/frxarfx7EgouLi6cP3+es2fPipZCK8jLy2Pjxo0cO3aMgIAAli1bhqenp9qFAfz7M9KpUyeMjIyIjY0lLy+Prl27YmlpqezSmuWlBkJCQgJffvkl3t7ezJ079zedfqQsT0LB09Ozac77yf54desvqoL8/Hy+/vprzp8/z8iRI1m8eLFafi7+ryfHr8nlco4cOYJCocDf318tDuR9aYGQl5fHt99+S0VFBcuWLaN3795q+Q0A/zum4O7uTkpKCmfPnsXd3R1nZ2dll6ZWcnNzWbNmDWfPniU4OJjp06er9OByS8hkMpydnSkuLubkyZMYGhri7e2t8l8aLyUQ7t+/T0REBGfPnmXRokWMGjVKrQZansXW1hZ7e3uuXLlCamoq3t7eWFpaqm3QvUw5OTls3ryZhIQExo0bR1hYGPb29souq1UZGhpibm5Oeno6SUlJ2Nvb4+zsrNKf/TYPhNraWmJjY9m/fz+DBg1i6tSpar2087+Zm5ujo6PDkSNHyMjIwNPTU6xm/BW3b99m06ZNnD17lqCgIKZNm6ZxYfCEtbU1enp6nDx5ktu3b+Pn56fS4wltHggXLlzg66+/xtbWlsWLF2tcs1pXVxdXV1csLCw4ePAgGRkZeHl5iVB4hry8PL755hsSExMZM2YMs2bN0ujTq+VyedMuyWPHjiGTyejatSsGBgbKLu2p2jQQCgsLWblyJbm5ubz11lvPvGRT3eno6ODl5YWlpSWxsbFcu3YNPz8/sRnqvxQWFvLNN99w5swZQkJCmDNnTrsITrlcjouLC48ePeLIkSMYGxvTpUsXlRxPaLNAKCsrIyIigjNnzjBlyhTGjh2rMafKPM2Tv3QzMzPOnDnDpUuX6NKlS7v4wDfH7du3Wb9+PefPnyc0NJRp06ZpdMvgv+nr62Nra8vNmzdJTk7GwsICV1dXlVuf0CaBUFdXx9GjR9m+fTsDBw5k5syZGjN6/Dw6Ojq4uLhgYmLCiRMnuHbtGp6ennTq1EnZpSnVTz/91DSoHBQUxJQpU7Czs1N2WS+VTCbDzMwMS0tLLly4wO3bt5sGoVVJmwRCRkYG3333HXp6evz+979vs6OxVZGuri7u7u6YmZlx/PhxMjMzcXd3b7ehkJuby9q1azlz5gxBQUHt5svhaeRyedMai7i4OIqKiujevbtKDbJr9ezZ85PDhw9z8eJFLly4QEpKCvb29i9cZFFREZs3byYtLY0lS5bw2muvtbtpOB0dHTw8PDAzM+PQoUMUFhbSrVu3F7qTUp0VFBSwdu1a4uPjCQoKIjw8XHShABsbG+7evUtsbGzT+gRVWbSkVV1d/UlhYSFmZmbU1dVRVVVFZmYmTk5OP7vJqDkePnxIVFQUR44c4fXXX2fy5MkaPW7wPFpaWnTu3BltbW3i4+PJy8vD1dVVZQ6AaWtPFqIlJycTEhLCzJkz220r6b8ZGhpiZ2dHSUkJZ86cwdHRkc6dO6vE+gQtT0/PT6ZMmcLChQsZNGgQvr6+fPPNN/j4+LRoirCxsZG4uDjWrVuHq6srb731VrttGj6hq6uLvb09dXV1nD59moKCAtzd3TU+FH766SfWrFlDUlISISEhhIWFtfvPwn8zNzfH0tKSc+fOkZaWhre3t0r8jOQymQxJklAoFDQ2NqJQKF6oiX/jxg02bNiAgYEB4eHharOHva3Z2NgwdepUQkJCSElJYcOGDdy6dUvZZbWZnJwc1q9fT2JiIsHBwYSFhbW7AcTmkMvl+Pv7M23aNLKysti4cSN5eXnKLgstLy+vTzIzM8nKyiI+Pp7k5GS8vLx49dVXm31UWElJCd9//z0XLlzgrbfeYtSoUSo3naJMRkZGuLm58fjxY+Li4rh//z7Ozs4a11LIy8tjw4YNTWEwZ84c0U14DrlcjoODA+Xl5Zw5cwZtbW26d++u1O30Wl5eXp9YWlri7e1Nhw4dsLCwIDQ0tNnNl6qqKg4fPkxUVBTBwcFMnTpVo662ai0dOnTAxcWFhoYG4uLiuHv3Li4uLhqzeCkvL4+vv/6aCxcuEBwczOzZs7GyslJ2WSpNJpNhYGCAs7MzpaWlJCUlYWNj03SBsTJoeXl5fTJ+/HimTZvWdCtSS242vnjxIqtWrcLBwYF33nmHTp06tbtZheZ60lJoaGhoGlPw9vZu8eCtqsnJyeHLL79sWnQ0depU0TJoAXNzc6ytrbl06RJxcXEMGDBAaesTtDw8PD7x8/N7oWPMbt68yRdffEF5eTkff/wxPj4+Igx+xZOWwuPHj0lKSqK6uhpPT0+1bVWlpqayatUqrl+/TmhoqBhAfEGWlpaYm5uzb98+7t69S9euXX922/XLotW7d+9PfH19W3wNVUlJCZs3b+b8+fO88cYbhIaGtlGJmsfIyKipmfjDDz/Q2NiIk5OTSi1QaY5r167x9ddfc+PGDWbOnMnEiRPb1XLk1iSXy7Gzs0NLS4uDBw8iSRKenp4taq23Bq3Nmzd/0qVLlxY9uK6ujri4ODZv3szgwYOZPXu2uKughYyNjXF2dqawsJAjR44gSRIuLi4v/QPwotLT01m5ciW3bt1i0aJFjB8/XinfaJpEW1sbDw8P8vPzOX36NIaGhnTt2vWlboLSWrdu3Sct/RDW1dVx6dIlHj9+zOLFi392tZbQfB07dqRbt27cvXuX48eP8/jxY7p166byi7kyMzP5y1/+QkFBAcuWLSMoKEhtuzyq5P8OMp47d46EhAS6dOmCs7PzS+uKv9BeBi0tLWxtbenXr9/PbsQVWkYmk2FiYoKXl1fTqrVHjx7h4eGhkv/AJEkiLS2Nv/3tbxQXF7N48WJGjRqlNq0adWFpaYm1tTUJCQlkZGTQr1+/Fi17r66upqioiIcPHyKXy1u0LPqFAkEul2NiYoK5ubkIg1bQsWNHXFxcKCkp4dChQzQ2NuLs7IyRkZFKDdKmpqby5Zdfkpuby5tvvsno0aPVbtxDXdjY2KCrq8uRI0eoq6vD09OzWT/r6upqjhw5wrfffsuJEyeora3Fzc2t2aGglItahF8yNzfHy8uLwsJC9u3bh66uLh4eHipzTH1GRgYrV64kPT2d5cuXExwcrJKtGE2ho6ODvb09JSUlHD58GAsLC9zd3Z/7D7uxsZEDBw5w7do1pk+fTr9+/UhNTeXmzZv4+vo2a22DCAQVYmJiQkBAAIWFhRw7dgwTExOVOFknOzubjz76iLy8PN555x2Cg4NV9ggwTfJkJ2RWVhZnz56lc+fOuLq6PrPVuG/fPs6fP8/ChQvp2rUr9vb2eHp6cvLkSbKysujTp8+vPlO091WMlZUVS5cuxcfHh82bN7Nr1y6qqqqUUotCoSAjI4OPP/6YBw8esHz5ckaOHKnyg56aQiaT4eDgwJIlSzAzM2Pnzp389NNPz3z9/fv3qa+v/9neEWtra7S0tCguLm7WM0UgqKDOnTuzbNky3N3dWbt2LQcOHKCiouKl1iBJEteuXWPlypUUFBQQHh5OYGCgGEBUgq5duxIcHExubi4bN27k7t27SJL0i9c9aTkoFIpf/P/mjkWJQFBRPXr04A9/+APOzs58/fXXHDt2jEePHr2056elpbFq1SoyMjJYvHgxo0ePVvsl1upKV1eX119/naFDhxIfH09CQgK1tbW/eN2TkJDL5ZSVlZGWlkZxcTGSJD01QJ5GjCGoMGtra3r06EFqaionTpzA1NQUV1fXNt8Nl5WVxf/8z/9w+/Zt3n77bYKDg1VmcLO9MjIywtbWlrq6OiwsLPDw8PjF5yA3N7dp2fPly5dZsWIFjx494vHjx9jb29OzZ89ffY5Mam50CEohSRKZmZl89tln/PTTT8yePZvQ0NA2me578qyPPvqIhw8fEh4eTlBQkAgDFdHQ0EBlZSVyuRxjY+NfdAOqq6s5evQo2dnZuLq6UlpaSkFBAVpaWowfPx4/P79ffYZoIag4mUyGlZUVrq6u3LhxgxMnTmBoaEjnzp1bdXDvyZjBp59+SlFREYsXL2bEiBFizECFyOVy9PX10dPTe+qYgI6OTtMemYMHD1JQUEBAQAAWFhbU1tY267Bj0UJQI9evX+eLL74gLy+PP/zhDwQGBrbaNfQpKSmsXr2a9PR03n//fQIDA8WiIzVVXV3N/fv3AZr2lzQ2NjZrDEgEgpq5du0af/vb31AoFLz99tsEBAT85tWi169f5+9//zsFBQUsXbqUUaNGianFdkrMMqgZLy8vpk2bRmlpKStWrODSpUsv/F41NTWcOnWKDz74gHv37rFkyRIRBu2cCAQ1o6enx5AhQ1iyZAkPHjzgH//4BxcvXmzx+1RVVXHo0CH+9Kc/UVZWxvz588WiI0F0GdRVbW0tx44d47vvvsPExIT333+/WdNK8L/nYEZERGBpacns2bPp27evONNCEIGgzmpqajh+/Dhr1qzBxMSEDz/8ED8/v+eOKVRXVxMbG8uGDRuwtrbmgw8+oHv37i+xakGViS6DGjMwMCAwMJDf//73FBcX8+GHH3L58uVnvr6mpoYDBw6watUqbGxsRBgIvyACQc0ZGBgwfPhw3n//fR48ePDMgcba2loOHz7M6tWr6dy5M++9954IA+EXRJdBQ9TX13P06FFWr16NjY0Nn3zyCZ6ensD/DiCuW7cOBwcH3n77bXr06KHkigVVJFYqaggtLS2cnZ3R1dXl7Nmz3Lx5s+mknMOHD7N27VpsbGx47733RBgIzyRaCBqmvLycXbt2sWnTJtzc3HBxceHMmTPY29vz5z//WXQThOcSgaCBKioq2LlzJ99++y0FBQUMGzaMDz/8ULQMhF8lAkFDlZWVkZSUxJ07d+jfv78IA6FZRCAIgtBEuad3Cm1GoVDw+PFj4N83Ain7oFZBPYhPiQZqaGggISGBw4cPI5fLGTRoUKtulRY0lwgEDdPY2MjJkydJSEigV69eSJLE1atXqa2tJTQ0VFysIzyXCAQNc/LkSc6cOcPkyZPx9fUF/n0xa3R0NAqFgkmTJim5QkGVia8LDZOTk8PDhw+bwgCgS5cuyOVyMjIymn36rtA+iRaChnnaGfySJLXobH6h/RKBoGGedga/TCZr0dn8QvslugwaxtDQEC0trZ9d6lJVVYVCoRAnKAu/SixM0jDFxcXs37+fyspKQkJCkCSJ06dPU1VVxcSJE7G3t1d2iYIKE4GggUpKSti9ezfx8fHIZDL69OnDpEmTRBgIv0oEgoZ6+PAhBQUFANjY2GBubq7kigR1IAJBEIQmYlBREIQmIhAEQWgiAkEQhCYiEARBaCICQRCEJiIQBEFoIgJBEIQm/x/6nYS/PciZZQAAAABJRU5ErkJggg==)
Maths-General