Maths-
General
Easy
Question
△ PQR is a right triangle with ∠Q=90∘ M is the midpoint of QR. Prove that
The correct answer is: Hence proved
![P M squared equals P R squared minus 3 Q M squared](data:image/png;base64,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)
![](data:image/png;base64,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)
As M is mid point of QR then, QM = ½ RQ
We get
—Eq1
Applying Pythagoras theorem For triangle PQM
—Eq2
Substitute Eq2 in Eq1
We get
![PR squared equals PQ squared plus QM squared plus 3 Q straight Q squared](data:image/png;base64,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)
![not stretchy rightwards double arrow PR squared equals PM squared plus 3 QM squared not stretchy rightwards double arrow PM squared equals PR squared minus 3 QM squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATgAAAASCAYAAADPP8KOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA6NJREFUeNrtW0+EVVEYP64xqyeS5EniGWmVmEVGkmGMkZHELJJkRIuRzKJdWsas0qJtWmV2I0kiGSMjkWQkYxhJyzajxXieuH1f8xtdZ8799949f9/5+Jk393zv3u93vt93z597nxDuWwr0COuEMeGX+R7/sHP2jUvUm6ecE8IC4bOnSfA9/mHn7BuXqDdPret5Erpi+KwbucR4I+dyu0hY87jjfY9/2Dn7xiXqzcC6mLFDWCZM5/j8IrwnrBCO5pyvjfV1x1K8fHyi5Bwz8DMd/yThNWEXo9cW4THhSI7/FOEd/BmriF3VJ65yDil/vtVL1JsUxAgCZ5KXc3zYbiBpsp0ivAIBW/GmSEyRfcjpfN3xc1xXCaOZY2cJbxS+84QvEGkCTGLf4qaiT1zlHFL+fKuXqLecIPgO/6nAJ1Gsn9sYLQ5ZjpfbNwjnCqbG3xTnGST+dEBOv6X/O4hRFUsLbR3p+qY5h5S/kOslSL3dq3ESVcISTFGLErYrHePAT1sqkGw83D6HeFS2hhE1bTD+QW5wLJxN6RgvI24VfGcePsIiZ116s80ltHoJUW/iPuEH4XyfCbtCeFngM41ped7eRFpS9GkF9BvvfjuPIOOS3wT2IVTnqRNDEze4YxAOx3NJatssmcK3MzxscdalNxNcdOpPR700Yd7pLa2IhxhBqiaMk/FVMSUVWMtfI2wXTE9Nj6ByvPvt17HWz9rbzH5CqjGmOnlbVPj0Kpynq7i+Ts6m9GYjf03qz8V68VFvlewpLvK8QgfsYB9hSRx84iN30oywZ2XxptLIdAafxzHLSAwVe5kdxsj/EXsWdQXXM8zZlN5c4eJSvQyl3qqOqEs1R9QyH07misWEpTVi5Sn5C3zmv3ca2jdrcg+uBdFljaf+x0uWDNuGOZvSmytcXKqXJs0XvWndEynzmcM1XFgiFLUnSAwvE35KhefKDU6e/rM9Itwu8GdRPbHMWZfebHMJrV5C1Nu/p1otjQljW7a0r5DWbF9AQhcbvik1dS6e3m9Jx05iXyfvsT23jVnmrEtvtrmEVi8h6s1Iwvjdn/UawrZ1g0uwVzLqwA1uDaP5iPj/IuV3cfBFSjZ+zL6B/ZL9Fy+n0OezDnAOKX+h1kvU2wAJY+O3pJ85XiC6lpX92AWx99SpC6wqxJM13pzmn/r04P9H7D258olzSPnzrV6i3qJ5ZbNYXvDPZ+4STsQuiRb1Fi0kS7Cc4N/6PYjdES0Evf0FNoSRjc18WJQAAAGSdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtc3VwPjxtaT5QUjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+PTwvbW8+PG1zdXA+PG1pPlBNPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+MzwvbW4+PG1zdXA+PG1pPlFNPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxRDI7PC9tbz48bXN1cD48bWk+UE08L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPj08L21vPjxtc3VwPjxtaT5QUjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtbj4zPC9tbj48bXN1cD48bWk+UU08L21pPjxtbj4yPC9tbj48L21zdXA+PC9tYXRoPr+X2+oAAAAASUVORK5CYII=)
Hence proved
As M is mid point of QR then, QM = ½ RQ
We get
Applying Pythagoras theorem For triangle PQM
Substitute Eq2 in Eq1
We get
Hence proved
Related Questions to study
Maths-
In Triangle
. Prove that![A B squared equals A C squared plus B C squared minus 2 B C times C D](data:image/png;base64,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)
![](data:image/png;base64,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)
In Triangle
. Prove that![A B squared equals A C squared plus B C squared minus 2 B C times C D](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKwAAAC/CAYAAABjczftAAAbLUlEQVR4nO3daVBUV8IG4Pc2NPuqoJFIQNBoBMWNRR0XCAqCQlDCIpHFpSKOyyRmKjOOpWMZrHEqmRHFaAQRQRYBt4CAiAsgipIgIiISCAIBAQVkh27o+/3IyDfJJMrS3adv93mq/IPNPa/dL5dr97nnMCzLsqAojuCRDkBRw0ELS3EKLSzFKbSwFKfQwlKcQgtLcQotLMUptLAUp9DCUpxCCyshjx8/RmhoKGpqakhHkSu0sBLQ0dGBkJAQ/PnPf8aVK1dIx5ErtLAScO3aNTQ2NmLmzJkoKSkhHUeuKJMOIG/q6+tx7Ngx+Pv74/Hjx3j48CFEIhF4PHpuEAf6LIpZQkICent74e7ujokTJ+LFixcQCASkY8kNWlgxqqioQHx8PLZu3QoNDQ0YGRmhvb0dra2tpKPJDYbOhxWfrVu3IikpCTNmzACPx0NnZycqKytx8eJFzJ8/n3Q8uUCvYcUkJycHOTk5+PLLL2FmZgaWZdHT04Nt27ahqKiIFlZM6BlWDFpaWuDn5wcTExMcP378F3+3bNkyGBsbIzIyklA6+ULPsGLQ2dkJW1tbeHp6/s/fBQUFoauri0Aq+UTPsGIgEokgEomgrPy/P//fffcdTExMYGhoSCCZ/KHvEogBj8f7zbJ2dnZi69atCAsLI5BKPtHCSlB8fDzu3r2LuLg4VFZWko4jF2hhJaS7uxtJSUkAgOrqaqSnpxNOJB9oYSXk7NmzyM3NBQAIhUJER0fjxx9/JJyK+2hhJaC1tRVnz55Fb2/v4NcKCgqQmZlJMJV8oIWVgMLCQuTn50NLSwsMw0BJSQl8Ph9RUVFoa2sjHY/TaGHFrK2tDaGhoWhra8PcuXOhqqoKQ0NDvPvuu7h79y6Sk5NJR+Q0Wlgxu3fvHlJTU/HOO+9g6dKlYBgGpqamcHJyAgAcO3bsF5cK1PDQwooRy7L4+uuvAQBbtmyBnZ0dBAIBBgYGsGHDBixcuBDff/89zp07Rzgpd9HCitHVq1eRkpKCiRMnwtXVFTweDyzLQigUwsTEBK6urgCAL7/8kk45HCFaWDFhWRYnTpzAwMAAli1bhunTp/9i4nZ/fz8CAgJgamqKsrIypKWlEUzLXbSwYpKVlYUbN25g/Pjx2LVr1+DZ9ZX+/n4YGRlh69at6O3tRWJiIl6+fEkwMTfRwopBb28vwsPD0dLSAhcXF5ibm//uYz09PTF27FikpqbSs+wI0MKKQXFxMXJzc6GtrY3t27e/9rHvvPMOdu7cCZFIhHPnzqGnp0dKKeUDLewo9fT0IDY2Fg0NDfD394eVldVrH88wDPz8/DB58mRcvnwZ2dnZUkoqH2hhR6m4uBgRERFQUVGBt7c3GIZ54/cYGRnBw8MDfX19CA0NpXfVDgMt7CglJCSgu7sbGzduhK2t7ZC+R1lZGX5+fpg6dSqysrJQWFgo4ZTygxZ2FB4+fIiIiAgYGBjAy8sLKioqQ/5eKysruLq6or+/H3v27EFfX58Ek8oPWthRCAsLQ2dnJxYsWIA5c+YM+/u9vb0xduxY3L59Gzdv3pRAQvlDCztC5eXlyMjIgL6+Pnbs2AFtbe1hH8PGxgZr165FV1cXEhMTJZBS/tDCjgDLsvj3v/+NmpoaLFy4EA4ODiM+1qZNm6Curo7k5GR6V8IQ0MKOwKNHj3D16lXweDwEBweP6lgWFhbw8fFBe3s7Ll26BKFQKKaU8okWdpgGBgaQlpaGyspKrFixAitWrBjV8Xg8Hv7yl7/AwMAAFy9exIMHD8SUVD7Rwg5TWVkZDh8+DIZhEBwcPKT3Xd/ExMQE7u7uaGxsxLFjx+hZ9jVoYYcpIyMDdXV1WLFiBRYsWCCWY6qqqsLHxwcGBgZISkpCfX29WI4rj2hhh+HZs2c4cuQIVFVV8cc//hH6+vpiO7ajoyM8PDwGl5unC/L8NlrYYYiIiEB1dTXmz58Pa2trsR9/5cqV0NTUxNmzZ1FUVCT248sDWtghamtrQ1xcHDQ0NODn5yeRtbKcnJywfPlytLe3Iz4+XuzHlwe0sEN0+PBhlJeXY968efDz85PIGK8uNVRUVJCYmIiCggKJjMNltLBD8PTpUyQmJkIkEsHX1xfq6uoSG2vRokWYP38+qqurkZycTK9lf4UWdgiuXbuGJ0+ewNLSEoGBgRIdS0VFBQcOHIC6ujpSU1NRUVEh0fG4hhb2DWpra/HNN99AKBTis88+g5qamsTHnDVrFpYtW4bS0lLExsaiv79f4mNyBS3sG2RlZaGgoACWlpZwdHSUypgaGhrw8fGBkpISTp06hebmZqmMywW0sK/R0dGBkydPgmEYfP7553j77belNvbKlSvh7u6OmpoaxMbGSm1cWUcL+xoXLlxAXl4e5syZg8WLF0t1bG1tbbi5uYHP5yMkJAR1dXVSHV9W0cL+joGBAXz99dfg8XhYtWoV3nnnHalncHFxgbW1NVpaWhAXFyf18WURLezvSEhIQGFhIaysrLBx40YiGQwNDbF582YoKysjPj4e1dXVRHLIElrY39Da2oojR45AKBRi5cqVUr12/TV3d3dMnjwZRUVF9FoWtLC/6fr163j06BEmTJiAzZs3E82io6OD3bt3A/h5plhDQwPRPKTRwv7Ky5cvERsbi87OTmzbtg1GRkakI8Hd3R3W1ta4desWUlJSFPrTL1rYX8nKysLly5cHb92WBZqamvD39wfLsoiIiFDo92VpYf9Lb28vzp07B4FAgE8++QSTJk0iHQnAz8sbubu7Y+HChSgoKEBeXh7pSMTQwv6X/Px8nD17FlOmTIGnpyd4PNl5eiZOnAhvb28AwM6dOxV2/1rZeUVkwFdffQWWZeHs7AxTU1PScf6Hs7Mzpk2bhsrKSoXd3IMW9j/y8vJw48YNTJo0CUFBQcNadkhapkyZAn9/f/B4PMTExKCjo4N0JKmjhcXPq2N/8cUX6OrqgouLC2bPnk060u/y8/PDhAkTkJubq5B3JdDCAsjOzkZ+fj50dXXh7+9POs5rGRsbIzAwEAKBACkpKWhvbycdSaoUvrB9fX1ITk7Gy5cv4ePjAxsbG9KR3ujTTz+FiYkJsrOzFW4ROYUv7K1bt5CcnAw+n0/8U62h0tPTQ2Bg4OD0R0XaDlShCysUCpGSkoIXL17go48+goWFBelIQ8Lj8eDp6YlJkybhypUrePToEelIUqPQhf3hhx8QGRmJsWPHYvv27eDz+aQjDZmFhQU2bNiAvr4+7Nu3T2Fuo1Howh4+fBgdHR1YsWIFpkyZQjrOsDAMg+XLl8PY2BiZmZm4ceMG6UhSobCFraqqwrlz52BoaIi1a9dCU1OTdKRhs7a2hoeHBwDg5MmThNNIh8IW9h//+AdevHgBZ2dnqd1cKAkbNmzA+PHjkZaWphAb1SlkYYuKinDhwgWoq6vDw8ODU9euvzZjxgwsWbIEHR0diImJkfstlBSysOfOncPz589hb28Pd3d30nFGhWEYhISEQFdXFzk5OXK/vJHCFba4uBgJCQlgGAaffPKJTM3IGilzc3N4e3ujvr4eMTExcr0dKPdfrWEQiUQ4f/48KioqsGjRIrEtSEwawzDw9/eHpqYmkpKS8OTJE9KRJEahCvvTTz8hISEBSkpK2LdvHzQ0NEhHEhtbW1ts2rQJLS0tOH36tNzeRqNQhY2JicGTJ0/g5OQ0oo3gZJmysjJWrlwJfX19hIWFobi4mHQkiVCYwjY3N+PEiRNQV1eHt7c3dHR0SEcSO1tbWzg5OaG/vx+RkZGk40iEwhT21KlTqKmpwfvvv49Vq1aRjiMRWlpaCAoKgr6+PpKSkuRyjoFCFLa6uhqHDx/+xa9NeWVvb48ZM2YMbiAibxSisBcuXEBtbS1mzZolM7duSwqfz8eePXugrKyMGzduoLS0lHQksZL7wjY1NSE+Ph4Mw2Dr1q1yfXZ95f3334ezszPKy8uRkJAgVzO55L6wZ86cQUFBAczNzeHm5kY6jtS8WsAuLi5Orpadl+vCNjU1DS7ts3fvXoU4u77yaqO6yspKXL16lXQcsZHrwmZkZCAnJwfW1tZwdXUlHUeqNDU1ERgYOLjJh7ws1Sm3he3o6MChQ4cgEong7e2tUGfXV2xtbbFo0SI0NDTIzYLIclvY69ev48GDB7CxscGHH35IOg4R48ePR0BAADQ1NREdHY2WlhbSkUZNLgvb1taGv//97xCJRPD09CSy3LusWLVqFSwsLFBWVobQ0FDScUZNLgt7+fJlFBUVYcqUKfjggw9IxyFKT08PAQEBAIBLly5xfnMPuStsT08PYmJiAADr1q3j3M2FkhAcHIw5c+aguLgY58+f5/RMLrkrbEJCArKzs2FoaDh4ZlF0DMPg448/BsuyOHPmDGpra0lHGjG5Kmx7eztSU1PR09OD4OBghb52/TV3d3fMmjULhYWFuHPnDuk4IyZXhb19+zYyMjJgamqKLVu2kI4jU8aPH4+dO3eiv78f//rXvzi77LzcFLa7uxtHjx5Fd3c3vL29YWhoSDqSzFmwYAFmzpyJe/fuITU1lXScEZGbwpaUlOD69eswNjaGj4+PXNxcKG5mZmbw9/cHn89HREQEBgYGSEcaNrl4Vfv7+7F//350d3cjICAAM2fOJB1JZq1Zswbvvfcebt++PfhuCpfIRWFzcnKQmpqKCRMmYMWKFfTs+hqmpqZwdnaGSCTC8ePHObdUJ+dfWZZlcerUKQA/b9luZ2dHOJHs+9vf/gZTU1M8fPgQV65cIR1nWDhf2MzMTKSnp0NXVxdbtmyhZ9ch0NHRQVBQELq7uxEVFYXW1lbSkYaM06+uQCBAfHw8mpub4eLiAktLS9KROMPX1xeGhobIyclBfn4+6ThDxunCFhYWIjMzE3p6eoP3MVFDM2XKlMEN6qKjo9HZ2Uk60pBwtrB9fX2Ijo7Gs2fP4OHhgalTp5KOxDlubm4wNjZGUlIScnNzSccZEs4WtqqqCsnJydDU1MS6devAMAzpSJzz7rvvYu3atRgYGODMgsicLWx4eDieP3+OdevW0XcGRkhJSQk+Pj4wMzNDWloabt26RTrSG3GysCUlJQgLC4Oenh7c3Nygrq5OOhJnzZgxA0uXLkVPTw9CQkLQ19dHOtJrcbKwUVFREAgEWLJkCezt7UnH4TQlJSVs374d48aNw927d3Hv3j3SkV6Lc4UtLS1FUlISNDU1sWXLFqipqZGOxHlWVlZYvXo1WltbER4eLtPLznOqsCzL4vjx46ipqcHcuXPxhz/8gXQkuREUFARlZWVkZGTI9HxZThW2vLwc165dg4qKCnbt2iVXCxKTZm1tjcDAQDx//hypqakye5blTGFZlkVSUhIeP34MBwcHLFu2jHQkucIwDIKDg6Gvr4/w8HA8ePCAdKTfxJnCVlVVDU6H27hxI50zIAHTpk2Dm5sb2tracPr0adJxfhNnXvX09HSUl5fDxcUFDg4OpOPIJQ0NDQQGBkJfXx+JiYmoqqoiHel/cKKwP/30E0JCQqCuro6AgACFXHZIWuzs7ODo6Ijnz5/jwIEDEIlEpCP9AicKm5CQgGfPnsHGxgZLly4lHUeuqampwdfXF9ra2vj222/xww8/kI70CzJf2FfXUyoqKggICKA3F0qBm5sbHB0d0dTUhIiICJlaeEPmCxsaGoqSkhJMnz6d89tscoWSkhI2bNgA4OdtTouKiggn+n8yXdhnz54N7lC9fv16jBkzhnAixeHo6IjFixejqqoKmZmZpOMMkunCpqSkoKioCHPmzMGmTZtIx1Eoqqqq2LdvH1RVVXH8+HGUl5eTjgRAhgtbV1eHqKgo9PX1Yf369XTOAAGzZ8/G4sWL8fTpUyQlJZGOA0CGC5ufn4/8/HxMnz4dq1evJh1HIenq6mLz5s1QU1PDmTNnZOJmRZksbGtrK/75z3+CYRh89tlnmDBhAulICsve3h729vYoKytDREQE6TiyWdi0tDTcu3cPlpaWWLRoEek4Ck1fXx8uLi5QUVFBWFgYmpqaiOaRycKGh4cDAHx8fGBubk44DRUQEAA7OzvU1tYS39xD5gobHR2NW7duDd4gR28uJE9bWxv+/v6Dq+yQXBBZpgrb2dmJqKgoDAwMwMXFBSYmJqQjUf/h4eEBc3NzlJaWIiUlhVgOmSpsZmYmCgsLYWJigs8//5x0HOq/jBkzBvv370d/fz/Onj2LZ8+eEckhM4VtaWnB6dOn0dbWho8++ghvvfUW6UjUrzg7O8PS0hK5ubn49ttviWSQmcLev38fWVlZ0NXVhb+/P+k41G/Q09NDcHAwACA2NhZdXV1SzyAThe3r68OpU6fQ3d2Nv/71r3SrIhnFMAzc3Nxga2uL3NxcZGVlST2DTBQ2NzcXcXFxmDhxIpycnOg7AzJs4sSJcHZ2BgDs3bsXHR0dUh1fJgobHh4OlmXh6emJ9957j3Qc6g38/f1haWmJkpISpKenS3Vs4oXNz89HSkoKTExMsG7dOqiqqpKORL3BpEmT4Ovri4GBAYSFhaG7u1tqYxMtbH9/P7744gv09PRg4cKFmD17Nsk41DB4eXnBwMAABQUFOH/+vNTGJVrY27dvo6CgALq6uvj000/ptSuHTJ48Gdu3b0dvby9SU1OltiAyscL29PQgOjoaTU1NWLNmDebOnUsqCjVCH3/8MYyMjHD58mVkZGRIZUxihb1//z5SUlLAMAy9m4CjXm1A3dnZiYSEBKlcyxIprEgkQnp6OpqamrBx40bMmzePRAxqlBiGQUBAAMzMzJCSkoLS0lKJj0mksPfv38fRo0ehqamJ9evXK8RmGvJ6fW5ubg4PDw8IBALs2bNH4ovIESnsq9st3NzcYGFhQSKCVDEMI7eFVVZWxpo1a2BsbIyrV69KfEFkqZ/aGhoaEBMTA0NDQwQGBkJbW1vaEaTmzp07EIlEKCsrw9KlS8Hn89+4KAWPx4OmpiYOHDiABQsWSCnp6NjZ2WHNmjU4dOgQQkNDJbtuLytlQUFBLAB25cqVbHd3t7SHl6rg4GAWAMvj8VglJSWWYZjf/cPj8ViGYVgArKqqKpuamko6/rDcuXOH1dHRYXV0dNj09HSJjSPVM+zjx49x7do1qKqqIigoSO4303h1GWBvb4/169ejv7//tY/t6+vD3r178fLlS84tJ2pnZwd3d3fExMTg0qVLWLZsGZSUlMQ/kMR+FH7Drl27WIZhWFdXV2kOS8yWLVtYAOyf/vSnIX+PlZUVq6amxqalpUkwmWSUlZWxurq6rJGREZuTkyORMaT2Y1xcXIzExESwLIuNGzdKa1iZMDAwMKTHCQQCmVvecjgmT54MV1dX1NfXIy4uDr29vWIfQ2qFvXnzJioqKrBkyRIsX75cWsNSUqSkpIQdO3ZAQ0MDFy9eRE1NjdjHkEphKysrcezYMSgrK2P37t10Mw05NnPmTKxduxYNDQ0ICwsT+28MqRT2/PnzKCsrw+LFizFr1ixpDEkRoqamhlWrVkFXVxfffPON2BeRk3hhu7u7cfLkSairq2PDhg0wMDCQ9JAUYY6OjnBzc4NAIBhcFEVcJF7YQ4cO4cmTJ7Czs4OTk5Okh6NkgIaGBry8vKClpYXY2FgUFxeL7dgSLWxjYyMiIyPB4/Hg7u6OsWPHSnI4SoY4ODhg3rx5aGxsRGxsrNiOK9HCJicno6amBjY2Nli/fr0kh5JpQ51HoKSkNPhYrs890NDQwO7du6GmpobLly+LbXMPiX3SVV1djaioKAiFQvj7+0NbW5vT7zEOF4/HG5w30NXVhebmZgiFwt99/KtPul7Ndnr1XHH5OVu8eDFsbW2RnZ2NyMhI7N+/f9Qz8xiWlcwWIZGRkdi0aRNEIhFsbW2hp6cnU7uRSBqPx8OjR49QW1sLHR0dvPXWW28sn0gkQm1tLQYGBjBr1iyMGzeO04VlGAYlJSWoq6uDhYUFUlNTYWpqOrqDSuLjs4aGBnb58uWDEzsAKOyfkfz75e05e9WDw4cPswMDA6PqlkQuCXp6ejB//nwsWbJEEofnDJFINOLfKjwej/PXsf+NZVnw+Xz09/dDRUVlxMeR2CUBRUkCt+awUQqPFpbiFFpYilNoYSlOoYWlOIUWluKUUb8PKxQKUVxcjPb2djAMA11dXZiZmUFXV1cc+TinsbERFRUVEAgEUFJSgp6eHszMzKClpUU6mlwYdWGLi4vx4YcfYubMmeDxeCgqKoKvry9CQkLEkY9zDh48iEuXLsHOzg4dHR2oqqqCnZ0d9u3bByMjI9LxpKqgoABXr15Fe3s7pk2bBjc3N4wZM2ZUxxx1YXNycmBqaoqoqCgwDIOQkBBkZ2eP9rCcJBAIkJ+fD19fX+zevRsdHR24ceMGduzYgWnTpmHnzp2kI0qFUCjE0aNHERkZCTs7O4wbNw5nzpzBy5cvsW3btlHd/j2qwopEIuTl5WH69OnQ09MD8PPHsoq6mXFdXR2am5uxdOlSqKmpQU1NDV5eXrhy5Qru3buHvr4+hVhhPCYmBqGhoTh48CA++OADqKiooK6uDgKBYNQfN4+qsF1dXXjy5AnGjBmDvLw83LlzBykpKYiMjBxVKK568OAB+Hw+LC0tB78mEomgo6OD9vZ2gsmkp7GxESdOnMCaNWvg5eU1+PW3335bLMcfVWGfP3+OtrY21NbW4sSJE/jxxx8V+o7Y4uJiGBgY/OLOiq6uLhQVFcHGxkYhzq55eXlobGzE6tWrJXL8Ub2tVVFRAT6fj+PHj+P06dO4dOkStLW1ERMTI658nFJeXg5jY2Pw+fzBr5WVlaGiogI2NjYEk0kHy7K4c+cOJk+eLLFVKUdV2JKSEowdO3bwmpXP50MkEo36f4JcJBAIUF9fDysrq8Gv1dfXY//+/ZgxYwYcHBwIppMOkUiEpqYmjBkzRmJv4434kuDVT5OWlhZKS0vR1taGI0eOoL29HYGBgeLMyAk1NTV4+vQp1NTU8P333+Pu3buIiIiAlpYWEhMToa+vTzqixPF4PIwbNw55eXlobW0dvKW/v78fQqFQLIv/jXg+rEgkwsGDB/Hdd99BKBRCRUUFlpaW8PX1xdSpU0cdjGvKy8vx1VdfobGxEcDP6/8vWrQIq1atUoiyvnL79m14eXnByckJ69atQ09PD27evAkHBwex3OZPJ3BTYjUwMICLFy8iNjYWQqFw8JO+wMBATJo0adTHp4WlJKK9vR3Nzc3Q1tYW62o/tLAUp9DZWhSn0MJSnEILS3EKLSzFKbSwFKfQwlKcQgtLcQotLMUptLAUp9DCUpxCC0txCi0sxSn/BwRqjojZqgOPAAAAAElFTkSuQmCC)
Maths-General
Maths-
In
and
prove that ![QM squared equals PM cross times MR.](data:image/png;base64,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)
In
and
prove that ![QM squared equals PM cross times MR.](data:image/png;base64,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)
Maths-General
Maths-
In the figure,
then find the value of x and y.
![](data:image/png;base64,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)
In the figure,
then find the value of x and y.
![](data:image/png;base64,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)
Maths-General
Maths-
Arrange in descending order of magnitude
and ![root index 9 of 4](data:image/png;base64,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)
Arrange in descending order of magnitude
and ![root index 9 of 4](data:image/png;base64,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)
Maths-General
Maths-
In △ABC, AD⊥BC Also,
Prove that ![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
In △ABC, AD⊥BC Also,
Prove that ![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
In the figure, AD is a median to BC in
and
. and DE =
![x text , prove that end text b squared plus c squared equals 2 p squared plus 1 half a squared](data:image/png;base64,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)
In the figure, AD is a median to BC in
and
. and DE =
![x text , prove that end text b squared plus c squared equals 2 p squared plus 1 half a squared](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
![](data:image/png;base64,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)
The Quadrilateral PQRS has angles at S,Q right angles and the diagonals PR, QS are perpendicular. Prove that SR = QR.
![](data:image/png;base64,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)
Maths-General
Maths-
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,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)
P and Q are points on the sides CA and CB respectively of a
right angled at c. Prove that ![AQ squared plus BP squared equals](data:image/png;base64,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)
![A B squared plus P Q squared](data:image/png;base64,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)
Maths-General
Maths-
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,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)
In △ABC, ∠B=90∘ and is the mid point of BC. Prove that ![A C squared minus A D squared equals 3 B D squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIkAAAARCAYAAADpEY/nAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAt5JREFUeNrtWE1kXUEYHfVEVZSoiCeqxBNZRTdVXUSEqKiKCFVR9UTporrIokRXWVQ31UVUlaonsogS0UVVlaqIqioV0UVUqOqym6jnqavC6xnO1THmzp33vJn7o4ezufky75y53/2+b0YI/2iTf8APYE0UD2XwUAiPx8Bb4G6BN7IMHgrhMSrBRkai/MjM4yS4U/DNK4OHnnpccogZAR+Ae+Bv8Ad4DxzQ4qrsdSMBzS45fC1thS1wEzyTEO/TwxT4mnsodR2Aq+CpFP1H3PNv4EtqDObxKoeYiiXmDvgKnGAvkzjNl7OmxI0yrhowQdL015jYai+W+m5z0+e1eN8etvmbfcqzs+AbR/2CH+daKI+yCnwB34JzCTHL4DOHtar8Qk4GTBAX/fL5RsLfroBNJfGz8BCj2YH+ee2ZV49PwQWwDj42/H2U5a3isJb84bHAG5umX2KFlTAJsiyfy9BD3Mq/WvQva8/WwZkQHi+w5EgMMRl0PHScV4TWD2P6hIt+wb48a1nnHTjdhYe2A9MgdS9yLrlk0T/HSiDbUsPwTrx4lJXhM+eKGLuGDNvP6YWSq37BF2Drvd/BwYwutGLaPsQDbRidCeXRVJ7u83JFHX6iQJvU6Vfooj/20LKscwL8mWGyD7BKfOJxVFj097EafOQY4NXjmDDfsk3yaCUUUc0cVhFX/RLnWWqTUHccyn21mxj9TBThoP8aryK8enxvMaUfJVvMxDyhE/0L7OFJkCej8Zz4MlVtk/7r2kvvucebvLhJwnNtgGqkTM2h0an+RxwMTVhNWSskxjlX6DDpbzAxvHisMqv6LTE3tEXlbd0heFf8u1k9Dl6m2OmAG9mN/hfaoCdb6EUeA59klBA7vLuocJ6Y4mBZN8Sq+gf5f3vaRVxPPW7y5dowbMjoGs/lTZb0X+CW5cjmC93oP1Ra0REHuA0en7PCBI/uEblt8aXqj1gphy0xefH4H2XFXzD8Dz/m/nIgAAAA5XRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5BPC9taT48bXN1cD48bWk+QzwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtaT5BPC9taT48bXN1cD48bWk+RDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+PTwvbW8+PG1uPjM8L21uPjxtaT5CPC9taT48bXN1cD48bWk+RDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+xGsG3QAAAABJRU5ErkJggg==)
Maths-General
Maths-
Maths-General
Maths-
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
The perpendicular AD on the base BC of Triangle ABC intersects BC in D such that BD = 3CD. Prove that
![2 A B squared equals 2 A C squared plus B C squared](data:image/png;base64,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)
Maths-General
Maths-
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
In an equilateral
the side BC is trisected at D . Prove that ![9 A D squared equals 7 A B squared](data:image/png;base64,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)
.
Maths-General
Maths-
![](data:image/png;base64,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)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAC2CAYAAABeQIarAAAgAElEQVR4nO2daVRUd5r/P7XJDiKbgAiiIC6gEgEVMYgomxFDRI1rjGljJ9OnJ93zZiZn5vT/nD7zZqY7M1km3Ymt0Q5RIQZQRBbZlE1URBEQRWQVBBGKnSqo+r+woZMOKspSC/dzDm+sW/d+6/q9v/tbnt/ziNRqtRoBAQ0h1rQAgemNYEABjSIYUECjCAYU0CiCAQU0imBAAY0iGFBAowgGFNAoggEFNIpgwAlCrVajUqkQ1pVeDsGAE4Ka9tpqSi/fouFhJ0OalqNDCAacEJ7QWJ7MyTNnSS99SNegpvXoDoIBJ4De6js8bm5DNMuCDnkXHfI+TUvSGQQDjpsuqu494nb7ArzmmmOprKS2rR3BgmNDMOB46WyhtuMBLeYG2M8zpr23jfKadnoFB44JqaYF6Dpdj5uov17MzcpMKk2MeNKoYkWkI09852NlZKhpeVqPYMDxoO6h6WELSqdQ9oZ54uUyk76SeDLanlDR3M0cc0OMhHfMcxFuzzgY6n5C25PHOCxbyOrVy1k4z4XlG9YyY0DFgxs1dHULw+EXIbSA42BIDbNMF2Hn6Ijt8NvW3IO1c5p5pFQyoBhCjRSRRlVqNyJhT8g4UD9dARGJRT/+J0aWQ0QiwXwvQDCggEYR+oACGkUwoIBGEQw4Qfw9Gkbo0bwMggEniAcPHpCVlUVNTQ0qlUrTcnQGwYATQG9vL+fPn+df//VfOX78OG1tbZqWpDMI84ATQFlZGdnZ2dy+fRsAPz8/Nm3ahEQi0bAy7UdoAcdJR0cHiYmJtLW1sWPHDqRSKdnZ2Tx69EjT0nQCwYDjpLCwkMLCQry9vfm3f/s3Nm/ezPXr1ykoKECpVGpantYjGHActLa2EhcXh1KpJDQ0FDc3NzZu3IhMJiM5OZn79+9rWqLWIxjwFVEoFFy8eJEHDx4QHBzMa6+9BoC3tzerVq3i6tWrZGdn09vbq2Gl2o1gwFfk3r17xMXFYWxszMaNG7GysgJAIpEQHR3N4sWLyc7OpqqqSsNKtRvBgK9AX18fWVlZtLS0EBoaypIlS37y+eLFiwkJCaGhoYHc3FyhFXwOggFfgdLSUjIzM1myZAnBwcGYmZn97Jj169fj6elJRkYGJSUlGlCpGwgGfEm6uro4d+4cra2thIaG4u7uPupxLi4ubN26lfb2dhITE2lubp5ipbqBYMCXJCcnh4yMDLy9vVm5ciVi8bNv4Zo1a1i+fDl5eXlcuXKFoSFhy/o/IhjwJWhpaSE5ORmxWMz69euxt7d/7vFmZma89dZbKBQKTp8+TV1d3RQp1R0EA74E2dnZFBUVERgYiL+/P1Lpi1cyvb29CQ0NpaamhtzcXPr7+6dAqe4gGHCMVFVVkZSUxJw5c4iIiMDGxmZM3zMyMmLnzp3MmTOHjIwMoRX8BwQDjoGBgQEuXLhAXV0dYWFhLFu27KW+7+7uTlBQELW1tWRkZNDd3T1JSnUPwYBj4ObNmyQkJODu7k5ERATGxsYv9X2pVEpgYCDm5uYkJCRw69atSVKqewgGfAHt7e2cPn2a/v5+goODsbW1faXzuLm5ER0dTV9fHxkZGTx+/HiCleomggFfwJUrV8jNzcXDw4PVq1czY8aMVzqPRCJh48aNeHl5kZOTQ1FRkTAtg2DA59La2srp06cxMjIiOjoaBweHcZ3Pzs6OyMhIlEolaWlp1NfXT5BS3UUw4DNQqVRcvnyZyspK1q5di4+Pz4REOK9Zs4Y1a9aQl5dHXl4eCoViAtTqLoIBn0FlZSVnzpxh3rx5REVFjUS7jBcTExPCwsKwtLQkPT2dBw8eTMh5dRXBgKPQ09NDUlIStbW1vPHGGyxfvnxCz+/r68umTZu4e/cu+fn5DAwMTOj5dQnBgKNw9epVMjIycHNzw8fH57nrva+CoaEhmzZtwtnZmbS0tGk9LSMY8B/o7u7m7NmzNDU1jZhkMli0aBERERHU19eTnJxMa2vrpFxH2xEM+A9kZWVRXFzM+vXrWbNmzZjWe18FmUxGQEAACxcu5MqVK5SWlk7LDe2CAX9ES0sLKSkpGBgYEBoaypw5cyb1es7OzkRHRyMSicjOzp6WraBgwL+hVCpJTU2loqKCoKAgfH19p2Rj+erVq1myZAmFhYVcuXJl2m3lFAz4NyorKzl37hyWlpa8/vrrzJo1a0qua2FhQUhICN3d3cTHx9PQ0DAl19UWBAPydItlTk4Ozc3NbNiwgaVLl07p9X19fUdiBi9fvkxf3/Sp8SAYECgqKiI2NhYnJyeCg4MxNTWd0uubmZmxZcsWLCwsOHfuHGVlZVN6fU0y7Q3Y1tZGcnIyarWa0NBQnJycNKJj0aJFbNq0icePH1NUVERXV5dGdEw108aAz0oceePGDQoKCvD29iY4OBgjI6MpVvYUAwMDwsLCmD9/PllZWSOZtn6MWq3WuwSY08KAvb29PHz4kPb29p/MtTU2NhIfH4+5uTmRkZHY2dlpUCXMmzePyMhIGhoaSEtLo729feSz3t5eampqaGpq0quR8rQwYFNTE0eOHOHEiRM0NTUBMDQ0RFpaGrdv38bX1xcvL68JX3J7Ffz8/Fi6dCmZmZnk5+ePxAzm5+fz2WefkZOTo1cbmzR/x6cAKysrTExM+P777zl69CjNzc3U1taSlpaGlZUVQUFBWFpaalomALa2tmzZsoX+/n6SkpKorq4mJyeHo0eP0traiqOjo8a6CZPBtMiQOnPmTN5//32GhoZISUlBLBYzNDREQ0MDe/bsYcWKFVrR+g2zYcMGiouLSU1N5ZNPPqGpqQkjIyPee+89/P399Srzqvbc9UnGzMyMf/qnf2Lbtm2kpKTw5z//GRcXFwICAjA01K6qlsbGxoSEhGBkZMTp06eRSCT88pe/ZO3atXplPphGBoSnwaDR0dG4ubnR2dmJpaUlJiYmmpb1M1QqFXK5nP7+fhQKBcuXL8fLy0vvzAfTzIAAxcXFNDQ0sHDhQm7dusWpU6eor6/XmumNgYEBMjIy+PbbbzE0NGTevHlcvXqVO3fuaFrapDAt+oDD1NbWcvr0aQYGBvjnf/5nWlpaSEtLY3BwkH379mlsEnoYhUJBbm4uX3/9NcbGxnz88cc0Njby5ZdfkpaWxsKFC5k5c6ZGNU4008qAWVlZFBYWEhoaSmhoKBYWFkilUrKysliwYAGRkZEa7Q82NjaSnp6OlZUV+/fvZ9WqVbS2tpKamkpWVhb+/v4EBgZq1YBpvEh+97vf/U7TIqaC+/fv8+c//5menh727NmDl5cXMpkMV1dXHB0dcXR0xNbWdtICUMeCUqnE3Nx8JLmlRCLBxMQEsVjMxYsX6e7uZsWKFaMmxNRVpkULODQ0RG5uLsXFxWzatAk/Pz9kMhkANjY2hISEaFjhU2xtbUfNvBAUFEReXh7Xrl3j6tWrREREaPRBmUj0py1/DqWlpZw6dQorKyvCwsJeOb2GpjA3Nyc6OhpDQ0MuXrw4spqjD+i9AXt6erhw4QLV1dWEhoaOOa+ftuHp6UlgYCClpaVkZ2frzXKc3huwoqKCCxcu4ODgwKZNm7Rmye1lMTIyYsuWLcyePZtz586NGi2ji+i1AVtbW4mJiaG9vZ2tW7dOeaTzRLNo0SLCw8Opra0lNTX1J9EyuoreGlCtVnPp0iVSU1NxdnZm06ZNmJuba1rWuAkMDGTJkiVkZWXpRYYtvTVgY2MjsbGxiEQidu7cybx58zQtaUKYO3cu4eHhPH78mPT0dJ2vTayXBlQoFCQnJ1NWVsa6deu0MuBgPAQGBrJx40aKi4u5evWqTm9o10sDlpWVkZiYyKxZs4iKitL4EttEY21tTVhYGAYGBqSmplJbW6tpSa+M3hlwcHCQCxcuUFlZyfr16/H29tarpathfH192bBhAyUlJaSnp9PT06NpSa+E3v3PFBQUkJWVhaurK8HBwROW10/bMDU1Zf369VhYWJCenk5lZaWmJb0SemXAlpYWTp48yf3794mIiMDb21vTkiaVJUuWsHXrVp48eUJubi6dnZ2alvTS6JUBc3JyyM/Px8/Pj6CgIK0MNp1IDA0NCQsLw8XFhcuXL1NRUaFpSS+N3hiwurqa5ORkpFIpmzdvfmYVS33D3t6esLAwOjs7uXDhAo8ePdK0pJdCLww4ODhIRkYGRUVFBAQEEBgYiIGBgaZlTQkikYjAwEAWLVpEQUEBN2/e1KlpGb0w4J07d0hMTMTS0pLQ0FBmz56taUlTyvC0jFKpJD4+nurqak1LGjM6b8D+/n4yMzOpra0lICCAZcuW6eXmnRfh4+PDqlWrKC8v58qVKzoTLaPzBszNzSU2NhZHR0fefPPNadf6DTM86W5ra0tWVhb379/XtKQxodMGfPToEfHx8bS1tREaGoqHh4emJWmU1157jeDgYMrLy3Umz6BOG/DatWsUFxfj7e1NRESEXkS7jIfhAYmTkxPnz5/n+vXrWrPd9FnorAGbmpqIj49naGiIzZs3691676vi7u5OSEgI9+7d48KFC1ofM6iTBhwcHOT8+fMUFhayZMkSfHx89CraZTyIRCKCg4Px8/OjqKiI4uJirZ6W0UkDVldXk5CQgJGREVFRUbi4uGhaklYxd+5ctm/fPjI/2tLSomlJz0TnDCiXy/n++++5e/cukZGRBAQE6OQmo8lm/fr1BAUFUVRURF5eHoODg5qWNCo6Z8DCwkKSkpJwcXEhODhY71JVTBTGxsZs2LABmUxGQkKC1k5O65QB5XI56enpdHd3s337dpYtW6ZpSVqNl5cXYWFh1NbWcunSJa2cnNYpA+bm5pKfn8+KFSsICAjQq0yhk4GpqSkbN27EzMyMkydPcuPGDU1L+hk6Y8CamhpOnTrF48ePCQgImLQqlvqCWq2moaGB/Px8amtrKS4uJi0tjcePH2ta2k/Qid67QqEgISGBlJQUzMzM6O7upqOjY9ouu72IgYEBCgsL+frrr7l9+zaLFi3Czs6O69evU1lZibW1taYljqAT2bEuXrzI//3f/yGVSpk7dy4lJSU0Njbi4OCAlZWVXu75eFV6e3tJSUnhD3/4A3K5nJ07d/LRRx8xf/588vLy6OrqYvHixVqTYUvrW8C6ujpOnjxJR0cHv/3tb1m3bh3nzp3jL3/5CzU1NXz00Uf4+PgIUzE8fe1evnyZr776CgsLC37961/j7++PWCzGyMiIRYsWkZOTg6enJ1FRUVoxea/VTcfQ0BAXL16ksLAQf39/QkNDcXNz4/Dhw/z617+moqKCY8eOTbsKk8/i7t27HD9+HKlUyr/8y78QEBAw8nawtrZm+/btWFhYkJmZqTX3TKsNWFxczLfffouZmRnbt2/HwcEBeDrHtWfPHnbu3ElVVRU5OTn09vZqWK1mUSgUXLx4kba2Nnbs2MGKFSt+doyfnx+hoaFUVFSQnZ2tFdEyU2bA4TpnI38vOL6pqYkvv/ySuro6du7ciY+PDyKRaORzY2NjoqOjsbOzIzk5mQcPHkzuD9By7ty5Q15eHh4eHqxdu3bULQkSiYTg4GAcHBxITU3VigxbU2BAFX0dj6m9d5fysnLKy8spr7hDfauc/meskQ9XCcrPz8ff358tW7aMuuLh7OyMj48P3d3dVFdXa/Wi+2Rz+/Ztnjx5gpub23P3Qi9evJgNGzZw9+5dsrKyNF6Vc/J77kPdlF84zadHz1KjHMLYSIJaNYhL0F72bN/GKhdTpKKffuXmzZucOnUKY2Njdu3ahZub26inNjAwYPXq1RQUFFBWVoa/v/+UVTrXJnp6eqiurh4ZaDxvhCsSiXjjjTcoKSmhsLAQX19fAgICnrONQY1KNVylU4RILEIsEj3j2Jdn8g2oVtD5SI2DWxjRe0NY6WFF791Czvwlg5LUObjuDsbhR/erpaWFb7/9lsbGRj788EPWrFnz3NNbWFggk8loaGigq6trWhpQqVTS1dWFiYnJmCp+Ojo6EhISwieffEJSUhJubm44OjqOcqSK/s4GSsvu8fCRHJXYDFuXhSx2c8TSaGL23UzJ3IVIPANTCwvsra2ZbWlDn8tc7O3tGTIzRCJ9+mTB0wpBKSkp5OfnExAQQHh4OGZmZs+M6hWJRCN/8PeawNoeBTyR/Pi3/7iP/Lx7IBKJWLt2LQUFBZSWllJSUoKdnd3PprJ6msu4lJ5C5u2H9A+KUXf3MWjijH/kFsJWe2A9Y/wt4eQbUCRBKuulpqyAE9/UctnehL6GGq7W2LJxlS1Ghn//ETdv3iQuLo6Ojg48PT2Bp0twz+rbGRgY0NjYSF9fHzKZjPr6eiQSyUg9XZFIpNdmFIlESCQS2tvbkcvltLW1UVVVhZmZ2XMTVw4/tO7u7ly+fJmzZ8+ycOFCFixY8KOjuii+cIFL1xWs2fkBG/3dkLWWkvztN1wryMLRxY61zrOYMc7fMDWztyI1g8oBejvlyI3VDIrVWMqq6Ot5iFzhjrnB09YvPz9/ZME8KyuLW7duPddAYrEYuVxOVVUVIpGITz75ZGSwMjg4iEqlQiaT6d1KiVqtRqlUolarMTAwQKFQcOvWLdrb2/nTn/6Eg4PDT1rD0RCLxbS3t1NfX49cLic8PBxXV9e/3yt5GcUPBpnp9Tp+y+djKgJsPQmO2smchz2YGIpfOJMxFqagDziEUmGC24oIIg5FsMxlJigeceUv/48SRSOdAyowePqjZ8+ejb29Pd3d3VhbW+Pg4PBcA6rVahwdHXF1daWwsJCqqip8fX2xtbWlqKiIhw8f4ufnh5OTk16MkNVqNWKxGLVaTXZ2Nu3t7axevRpHR0dqamoQiUS4urpiZ2fH4ODgc00oEono6elBIpHg5OSElZXVT1/hXY9os7LBysURU4O/P8BmLj74TGAA+tT0AdWDdHe0UN/UgI2FAkVLNZUNM5Ea2mD+tx8tFosJCwujrq6O77//nqVLl7Jnzx5MTEyeG80rlUrp6uriq6++oqKiYqQK0meffcb169fZvXs3AQEBDA4O6sXrWCwWo1KpUKlUVFVVceDAAebNm4dUKqWtrY3Dhw/j4eGBQqF45jlkMhkdHR3813/9F66urrz77rs/m2dFaoNVXxszuvsYVKkYnrFTKXrpUwwiNjDGQCYd9zze5BtQbIDlHEN68i5z/JOrxJnIQK3C8bU32LpuNfYmP51c3r17Ny0tLWRlZeHh4UFwcPAL1yzVajUmJibIZDKMjY0xMzNjxowZiEQijIyMMDAw0LtcMcMlvGQy2chATaFQIJPJmDFjBjNmPLt31tfXx9mzZyktLSUqKmok2+qPEVm74KzO5c6tm9R5O2HhYo5kqJ3KrDgKGiTMX78FX1cbxhuROQUGNGFh8BY+8lxNZ98AKhWIJFIsHecy28rsZwJsbW3ZvXs3n3zyCTExMZiYmLBq1arnBhsolUp6e3uRSCTMmDFjpI80Y8YMvU3TYWFhQUdHBy0tLSxcuBB4Oh/4oqjn/v5+YmNjiYmJYdWqVURGRo6+n1pqz9KAOVSeu0V6qoiWJfOQtlSQn1eG0i2Q18xNmIhQhil4BYsxtLDGxWLsMWhLly7lnXfe4Y9//CNHjhzB0NDwual25XI5dXV1GBoaYmVlRUdHB83NzTg4OOhcWa6xYm9vj1KppLGxcaQfV1JSwt27d1myZMmoLaBarSYjI4OYmBjmz5/Pnj17mDt37jOuIGLB2rc4YD2Tb06ncDTzBwbFNnise4PtUYEstTZiIqajtTaGyd/fH7lczldffUVMTAyWlpbMnz9/1GPb2tpobW1lwYIFmJiYUFJSQm1tLSEhIXprQHd3d+zs7CgrK6OzsxNfX19SUlIoKCjAz89v1K2qV69e5eTJk9jZ2fHee++xePHiF1zFAFuPMH778UaGVGpAjEQqQSKeuJUQrZ2fEIvFhIaG8vbbb3Pnzh3OnDkzak2MwcFBrl27Rnd3N4sXL8bExISKigqGhoaYP38+pqamGlA/+cyfP5/FixdTUVFBUVERTk5OeHl5UVxcPGp0UEVFBUeOHKGvr4/9+/fj6+s7xukpERLpcL9SOqHmAy02IDwd4b755pts3LiR5ORkEhMTf3JjlUol6enpxMXFYWNjg4+PD1VVVeTl5eHs7PzMNWR9wNDQkNWrVzM4OEhCQgJyuZyIiAgsLS1JSEjg2rVrI7MHTU1NfP755zx48IC9e/eybt06rekba31IvlQqxdXVlcrKSjIzM7G1tWXevHkMDQ2Rnp7O559/jlqt5vDhw7i7u3P06FHKy8t58803WbVq1UhdYH1k1qxZtLa2kp+fj5GREevWrcPa2pq8vDzy8vKQyWSYmJhw4sQJUlJS2LFjB9HR0Vq1m1Ck1pHJsfLycv77v/+bvr4+goKCePjwIampqVhbW/OrX/0Kb29vvvvuO06dOkV4eDiHDh3CxsZG07Innfr6ej7//HNKSkrYsWMHISEhlJWVceTIEaqqqpBIJAwNDbFr1y727t07pmCFqUTrW8BhbGxscHR05MaNG8TExHDjxg38/f351a9+hbOzM7GxsZw4cQIvLy8OHDgwbfLFWFhY4OTkRGVlJampqXR3d+Pj40NwcPDIdswtW7Zw6NAh7O3tNS33Z+iMAQEcHBwwNjbm3r17zJo1ix07dmBmZsaxY8dISUnB39+fQ4cOsXjxYr1b/30e1tbWLFiwgLa2NhISEqioqEAkEnH//n3c3d15//33tbY/rDOv4GHUajWZmZl88cUXdHV1oVarGRgYICIigv3792vlUz5VtLa2EhcXx7Fjx7h16xarVq3iP/7jPwgMDNSaQcc/orXzgM9CJBLx+uuv09HRwe9//3sMDQ35zW9+Q3h4uN4XpnkRNjY2REVFUVZWxuDgIDt37mTlypVaaz7Q8mmYZzFcjGY4WKG5uZmBgQFNy9I4crmchIQEamtrOXDgwMg2TG1GJw0IT4NR3377bVasWEFSUhLp6enTemtmb28viYmJnD17lmXLlrF161adKNSoswaEp4OSffv2sWDBAuLj48nJyZmWLeFwJtSEhATc3d3ZtWuXzuTM1mkDAnh6enLw4EGkUilxcXHcuXNH05KmnLy8PP70pz9hYmLCe++9x5IlS14YEa0t6LwBAby9vXnnnXfo7OwkPj6e+vp6TUuaMu7du8fx48eZMWMG77//PkuXLtW0pJdCLwwIjJRozc3N5bvvvtPqxNwTRW1tLV988QV1dXVER0fz2muvaVrSS6Nz0zDPwszMjF27dvHkyRMyMzOxtrYmOjpab4vXPH78mJiYGEpLS9m6dSuhoaFatcY7VvSmBQSYOXMmBw8exNPTk8TERPLz83+2n0StVjM0NKT1m5RUKhVDQ0Oj7mPp6uoiLi6O7OxsIiIi2Lt3r85uyNcrA8LTSOF9+/Yxa9Ys/vrXv1JQUPCTPbJNTU0kJCRw6dIlenp6NKj0+VRWVpKQkEBlZeVPHhaFQkFiYiKxsbEsX76ct956S6crBeidAeFpdvj33nuPx48fc/ToUaqqqoCnS1V//etfOXbsGFVVVfT29mrdbjmVSoVSqaS1tZUffviB//3f/6W8vHzk8+zsbGJiYvDw8ODAgQM6nytbp4IRXgYnJyfEYjE5OTn09fUxc+ZMvv/+e9LT03n99deZO3cuycnJ9Pf3M3fuXK3JsNrS0sI333zDw4cPcXZ2pqCggLy8PGxtbWltbeWzzz7DyMiI3/zmNzo34h0N7bjrk4BIJCIyMpLW1lbOnz9Peno6KpWK8PBwPDw8OHfuHHK5HH9/f60KWrWwsEClUnHu3Dk2btzIBx98wOnTp/n3f/93RCIR1tbWHD58WC/MB3r6Ch7G1NSUDRs2YG5uTn5+Pg4ODtjb25OUlERfXx+//OUvWbdunVaFbhkaGnLo0CHCw8MpKChgYGCAHTt2IJfLuX79OsuWLcPLy0urNI8HvX0FAzx8+JD4+Hhu376NoaEhvb29XLt2DVNTUw4cOMC6deu0qvUbRiaTMWfOHGpra0lOTubu3bvA0/XvgYEBnJyccHZ21uool7GiH4/RKDQ1NXH8+HHS09MJCQnh/fffRy6Xc+PGDRYuXMjKlSufmz1A0wxXvBwe9Xp6evL73/8eqVTKkSNHuHnzpqYlTgh6aUCFQkFSUhIFBQWEhITg5uZGSUkJCxYswN/fn9LSUq5fv661FSTh6VxfSUkJUqmUlStXcvfuXWpqaggLC6Onp4evv/6a0tJSrRrBvwp6acChoSGsrKx4++23cXFxIT4+nv7+fj7++GP+8z//k8HBQY4dO0ZFRYWmpT6TrKwsTpw4wfLly/njH/+Ij48PcXFx1NbWEhkZiaurKz09Pc/NA6gL6GUfUCKR4ObmhrW1NbGxscjlcn7xi1/g7++Po6MjxsbG5OfnU19fj6urq9bFzWVnZ/PFF19gbW3NBx98wMqVK1m2bBkqlYqcnBycnZ15++23cXNzQyqV6kzky2jopQGHM4cOZ0rdsGEDvr6+yGQyRCIRLi4uiEQisrKyaG9vx9XVVWsih2/dusVnn31Gf38/Bw8exNfXF4lEgrGxMR4eHtjZ2TF37lzmz5+PkZGRTpsPdHBT0sswnEdPIpH87D9KLpfz5ZdfkpaWxubNm9m3b5/Gi/jV1dXxxRdfUFVVxd69ewkJCRk1wEClUv0kN7Yuo5d9wGHEYvEzX1EWFhYcPHiQZcuWcfbsWTIzMzVa0LmtrY0TJ05w/fp1IiMjnxvdIhaL9cJ8oOcGfBE2NjZ8+OGHeHp6cu7cOYqKijTSqe/o6ODEiRNkZ2cTEhJCeHi4VhQSnAqmtQEBFixYQHR0NL29vRw5coSSkpIpvb5arebChQvEx8fj4+PD3r17Nd4VmEqmvQEB1q1bxy9+8QvkcjmnT5+e0rpz2dnZnDx5End3d/bs2TPtinALBvwbgYGBvPXWW5SVlREXF0dzc/OkXk+tVnPt2jWOHTuGlfGrwVEAAASGSURBVJUVhw8fHkPCSP1DMODfMDQ0JDIykjVr1pCSkkJcXBxPnjyZtOuVlpby9ddfI5fL2bZtG8uWLdObgcXLoLfhWK+ChYUFhw4dor+/n8zMTJycnAgNDZ3wAUFDQwPfffcdzc3N7Nmzh6CgIK0MipgKhBbwH7CxsWHXrl3MnDmTb775hitXrkzoeuvg4CA//PAD169fZ/PmzYSFhenkZqKJQjDgKCxcuJDdu3ejUqk4evQoxcXFE2JCpVJJbGwsZ8+eJTg4mLfeektvc1iPFcGAoyAWi3n99dd59913aWlpISYmhurq6nGdU6FQkJKSQkxMDEuXLmXbtm06u5NtIhEM+AxkMhlhYWEjI+NTp07x8OHDVz5ffn4+x48fH3nFz5s3bwLV6i7CIOQ5GBgYsHv3bp48ecLZs2eZNWsWe/bseW5F8tEoKyvju+++w8DAgHfffZeVK1fqTUj9eBHuwgswMjJi3759+Pn5ERcXx/nz5+nr6xvz96uqqvj0009paGhg9+7drFmzRjDfjxDuxBiYPXs277zzDjY2Nhw9epRLly6NKZq6s7OTb775hqtXrxIVFUVQUJDWbP/UFgQDjpGlS5fy4YcfYm5uTmxsLDdu3Hhu4IJcLufEiRPk5uayY8cOoqKipk2AwcsgGHCMiEQiAgICOHjwIE+ePOHMmTPPTAM3NDRESkoKycnJBAYG6nTulslGMOBLIBKJCAsL48033yQnJ4f4+Hi6urp+coxarSYrK4uTJ0/i6urKvn37cHBw0JBi7UfokLwC27Zto7m5mcTERGbOnMmOHTswNjZGpVJx+fJl/ud//gczMzP2798vTLe8AMGAr4CxsTE7d+7k0aNHJCUlYWVlRVhYGI2NjZw5cwaZTMb+/ftZvnz5tAwweBn0ek/IZFNWVsann37KwMAAISEhlJeXc+vWLd555x02b948bQMMXgbBgOMkPz+fo0ePcu3aNWQyGfv27WP37t3CoGOMCK/gcbJq1SqUSiUmJia4uLgQFRUlmO8lEFrACUCpVNLZ2fm0Pq+pKRJhpWPMCC3gOFD1d9HyqIX2rj7UYjEqtZoZZrOYbWuDmaEUYfjxYgQDvjIqeu4X8+3n31HU1IHRLBMkKDCa7cbasGiCfRZhYyhY8EUIBnxlVPR39aBUzGHjtp1sDPPCjG4q08+RlpWL1GAmYa85YKr7KfwmFaGz8sqoUSNGZmDKLCtb7KyssLJyZk3YJuahoP5qBY86p1/dupdFMOA4EAGo1ajUKkZGchZWzDGSY/i4id6uQbS7GonmEQw4Xn7WzRtCBajEolE+E/hHhD7gOFCjBkSIReK/e629ltJeKXIbe4zMZMIT/gIEA74yIkQiNcr+Dpoa63hQZ44ZXdzJSKdlxixWrl2Kg4X25qDWFgQDvjIiDC3MMTJtJff8UQovGyNRKzGZu5QNbwSzYZEtxsIr+IUIKyHjQK3sR97Rjry7j0GVGtRgMHMW1pYzMZQI7hsLggEFNIrQRxbQKIIBBTSKYEABjSIYUECjCAYU0CiCAQU0yv8HnWQN9PKUarMAAAAASUVORK5CYII=)
ABC and DBC are two isosceles triangles on the same base BC. Show
that ![straight angle ABD equals straight angle ACD](data:image/png;base64,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)
Maths-General