Maths-
General
Easy
Question
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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)
The correct answer is: Hence proved .
Aim :- Prove that ![A Q squared plus B P squared equals A B squared plus P Q squared](data:image/png;base64,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)
Hint :- Applying pythagoras theorem to both triangles ABC, ACQ,PCQ and PCB
find the equation, add them and substitute proper conditions to prove the condition
![](data:image/png;base64,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)
Hint :- Applying pythagoras theorem to both triangles ABC, ACQ,PCQ and PCB
find the equation, add them and substitute proper conditions to prove the condition
Explanation(proof ) :-
Applying pythagoras theorem to triangle AQC we get ,
![A Q squared equals A C squared plus Q C squared minus Eq 1](data:image/png;base64,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)
Applying pythagoras theorem to triangle PBC we get ,
![B P squared equals P C squared plus B C squared minus Eq 2](data:image/png;base64,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)
Applying pythagoras theorem to triangle ABC we get ,
![A B squared equals A C squared plus B C squared minus Eq 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAATCAYAAADrhC08AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAyhJREFUeNrtWVGEVFEYPsYYSWKtrDESWStJekuSFfuQNQ9ZkpUk0UNP+7Ckpx7SS3pIeklG9mFFkqyVSLIyEhnZh5Ul6am3lSRjLdP/m2919uycOf+Ze++5dzgfHztnz7nznW/+c85//qtUduiAm8QmcVwNF4ZV/7D7ngtKxBvEVtQfdRcd7ag/6i4yJokrUX/UnQXmBKt0i/iD+I24RKwafarIjQ4XSLeCnnvEL8S/mMMd4khO+iVeFkl3pw99cJb4GnNhD9aJD4ijksEXkXyXLf8fh1E62Kyn2ucJ4rLF7Kzg0s2Yh64zyN0YBxHceeiXeFk03Z2UnvOeOEOsaG0niG9cA3lVrhLfEs9b+nD7otE2o7VVsUL2BwxQie6bxCeCZyXR7/sDurwMpTuPILXht6vDY+Is8QrxkaXPbRinY4F4Dn+zUUcCpycu3RM4SsuCZyXR7/sDurwMpTvtOU7ihNiE/qvCcZyifO3X4RSOCsYYHt4Lz7EDlLA9N4xc0CdX6QjogkT3fWG+qlSyXMs3SF1ehtKdZpDyQlkjHsPno8QXjnFjCGTOS6dtnXilfkaes42WZWWuayb80VZ9HpDqXlNhitu+geHyMpTuNC5O22jgVJN4Yz5jznXszBttd1W3KKyjBDMVEt4p4kccS3lAoruksqsZJjkJXF4WVbdrIf4k7vEcN4IT5RNShZ7bc8uSVywZbSeJ74y2SyiNhDZLqrsiScZz2EldXobUneYctxJ4sw+Bugsf+gSIWdKZxXau47Lw9pk2fHTzjrW3YEEq8TKU7jTn2NbKZIN4s+v0uK66BVQbnhmJ7EMkuEqQg2QJX92NHmlB3kEq8TKU7jTnyPXP00bbqNCb48jTd9TVVrHF2nDNCIaXWnJ/gHgBpYZKQJMG0X2IuEG8pf6/oeG8qY5AmMohSCVehtKd5hw5jeF6dQ07Kmtt9hi3gjmX0Y/fQH1X3TLijvJH3fGFNSOyN7QjtY0dqxbYpEF0K9ySF5Dnsf5fKI1M57QjSb0smm7J/YEvf68wrybKa2aQ8tuzZfRpYweuq4iIAqcJERExSCMivG/tLvwDf9hL+C5bPd4AAAD6dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPkE8L21pPjxtc3VwPjxtaT5CPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz49PC9tbz48bWk+QTwvbWk+PG1zdXA+PG1pPkM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5CPC9taT48bXN1cD48bWk+QzwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW8+JiN4MjIxMjs8L21vPjxtaT5FcTwvbWk+PG1uPjM8L21uPjwvbWF0aD5UWFKCAAAAAElFTkSuQmCC)
Applying pythagoras theorem to triangle PCQ we get ,
![P Q squared equals P C squared plus Q C squared minus Eq 4](data:image/png;base64,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)
Adding Eq1 and Eq2 we get ,
![A Q squared plus B P squared equals A C squared plus Q C squared plus P C squared plus B C squared](data:image/png;base64,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)
![A Q squared plus B P squared equals open parentheses A C squared plus B C squared close parentheses plus open parentheses Q C squared plus P C squared close parentheses left curly bracket text substitute Eq3 and Eq4} end text](data:image/png;base64,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)
![A Q squared plus B P squared equals A B squared plus P Q squared](data:image/png;base64,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)
Hence proved
Related Questions to study
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,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)
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,iVBORw0KGgoAAAANSUhEUgAAAI8AAAARCAYAAADkD/+gAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAqhJREFUeNrtWUFLG0EYHSSEIqHgQUIIIgSR4Kk3KSK5iIh4kIKUIEWK4KGnHgKlJw/iRTyIeBEJ4kGEICIleCk9iIgUihQPPRR68A+ISJBQhPQb+sRh2N2ZZWdmsyYPHmRnh9n3vv125psJY/GjBf4lnhOH2PNEUn0mQncP8QPxkj1vJNVnInQ3WWeg2dVtFiXiaQckTlJ9euoeIx4S77C2/STOhxj0o0a2PhCviX+IX4g5qU8Oa2rBgmnb/hh0r2Hse3hdIfY59Bk25kZ082wqEzO4HkHHsobIt3ghKZ/7QxAmgovbFa6HiXUfcyZg0x9HBfrHURtwDCDpXPoME3OrugeJV4o+fejzlTjr04e370ttb4Q2LuiE+NLxFGzK3yfijsbzovhsheyvirkT3ariaBtf7wJxy6fPMoSK2CNO4TcXVmzT4k/lbxhLQkrjWVF8hk0eVcyt636NqT3ofh2/sxDjhRq+BD4tviJWpRqi5UHVmUMQXfpb16yHWEStYZNHFXOrul8Qv6PQ9ALP2B9YHx9x6ZOhv4WHNoTsjxOm/P1ibg7NwiaPKubWdPN1/pg4qZgWK1LbKg6R5IOlBn6niRPEC0ybccGUvx6LZx5RZlhVzK3pLiCwQVlZZN6njCVsB0WMEr9JbfPYGroOqml/aWz9WZvNPKqYW9FdRPXdq+h3FvDi5C1tGeutiHeaVX4S/DU0xnOdPDoxN6o7iyJLVX0vETcC7h8Qp4XrTeJ7qU9V83zFJGz5q3osb3Enj07Mjequa2zHcjjzyAT0WZSCfyQUa/3EORxepR0njy1//KzohviZPZ3I8mJ8Bi9oIobk0Ym5Ud06NUQNgwchj0r/ETfCOE18ufkYlixb/hjqpz3UEXy8W/b/r5DpmDYEujFvN91ddBL+AU7LHYvEvvkPAAAA6HRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj4yPC9tbj48bWk+QTwvbWk+PG1zdXA+PG1pPkI8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPj08L21vPjxtbj4yPC9tbj48bWk+QTwvbWk+PG1zdXA+PG1pPkM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5CPC9taT48bXN1cD48bWk+QzwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+Bfvh+gAAAABJRU5ErkJggg==)
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,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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)
![](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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)
Maths-General
Maths-
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Classify whether the following Surd is rational or irrational , justify. 3√24− 5√5
Maths-General
Maths-
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Classify whether the following Surd is rational or irrational , justify 4√5+ 9
Maths-General
Maths-
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
PQR is a triangle in which PQ=PR.S is any point on the side PQ. Through S, a line is drawn parallel to QR intersecting PR at T. Prove that PS = PT.
Maths-General
Maths-
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , justify 8-√48
Classify whether the following Surd is rational or irrational , justify 8-√48
Maths-General
Maths-
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Classify whether the following Surd is rational or irrational , Justify.√47+√8
Maths-General
Maths-
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
In the figure, sides QP and RQ of a
are produced to points S and T respectively.
If
and
, find
.
![](data:image/png;base64,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)
Maths-General