+0  
 
0
642
3
avatar+101 

A rectangle is inscribed in a unit circle. Find the largest possible area of the rectangle.

 Mar 25, 2020
 #1
avatar+2094 
-1

Hint:

 

data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAADcCAMAAAC4YpZBAAABQVBMVEX+//z///////2rraqEhoOLjIri4uBfW9eipfC1tewAANHx+/GR14rp6fcAANUqI9fY2fXp9+el3qEAAACcm+b29/Tz9PHFx8Tp6ueP0Y7Q0s9YvFTZ2tfS69B8fnuWmJXe9NwArACjpaK+v7y1t7SSlJHMzcqmqKVGR0WGh4VZWlhtbmxRUlAzNTN0dnPy8/y+6b1jZGIith0lJyQOEQ62tvrG68U4OTgoKScaGxpAQj/Pz/zGxvvV1fvJyfsAALlzdGg1OCNfvlxKuEXLzOQ+OcQyMHVVUb8qI7opKqNBRGUAAL6Wme9YWoSQk9VydexkYegAAENrbZZhY1KJiOJMuUltw2yD1H0/vzit4qwZtxZ7euBwcn4AAGhkYZkSEGySk6YAAJFxcsIZGw4xMmwsLg4AACzh4uljY4KhodI9PovgeUayAAATWklEQVR4nO2dCXvjtpnH8b6UuJ7ISiwpPIZDk4pI6j4jWZctTzPT7W7bdK/uHE7bbLfd+/t/gAVIXZZIiSRIyePH/ycZ2SYJ4idcL4AXACEvetGLXvSMhcD+R4J47pikKNQVQNWWQRefMSZYMxWaAwmcJpw7LukJpZmlT0WQuiXynBNz3qhXAPRZ23zGiQlmiaYiSi1dfcZpiWpJpIkIWfEZJyVCpssKJKV8vkmJamOms0R81pSgdTU3pz5rSgLgFceIlIcsJTxsRp3TyIpEiZIsBd6NkiQHV2QHH01dUShR1uyKHHQ7aEpWC8JESbOcwKupK1JaWiLYmYCogk0NqXYQByg6aIFXU1ektLQ0sLpBlIoNUA+krFogzr8ISlplEVMPBAGwhUAOerVW+zIoadmrrG37vSiDbh3AAFU4X7cgJCW63W0ULZBXDyobJDcEVHXwpUT2H8gCnK+SDUcJtJGQZVArWlVY3g7CqrZFVIH+A4KiVWH5F0/ejSqACHJF04Lzc8pCZq0fxUTRFhQ7K1pGpqt7CUehVA8DiWIqIJuakTF8OnGoKg3Fzuj06skpEVyhl5arXwJlQ3UOFdm9bRWCoHr2DIp6RgDFWF/EatdwlXX7dFV5LivC9qPpi+Yj9j5Jt2qm08gYxrxFo+M4pqCoLqqPnUbtFqhlt74GUOgTTcNxHMaBtAGB5lYxhbXYb6rdPSWgO2YnSapuNicdpnqzZWTbRjYzaM/Z75NJV1BliewlK41lVgdpE44ky1JFl2W3KgKlDbDV4qNe8SS4aQmNQ1Vv0qJRFRWzOeu0GqZdFeXl151Vl1+7rCuCk2nOpl1LkR99+ShW5bZKrE0diW65BC/ZIVsDccseoCXRU1V2q9dBoFGYsFguFYVWp9QUqiLxcuaSfVXHejkZZL3qdEptw9oqqCB07YxtPW4IQFiNpIDY0gbb9Q6uMqyblFr9NC0ITRjRHHbaNZWhPC53uy0JiyG1yhvtYV1TySbrItlp08FeUqKkSnL30ODRKSARRLs7MiqiW7XsXvVrL91kVZz6MGvJwTXv6gq1wqWqcwAlfUgaX9WYzRSRBEQ30CqgKao7pbl5tH5E2RbsM/YdKaNstactbTebbumA7cNStNIsmQGG26P7zgdJ3241R7QqPBTJIxYeEMUomSHMozOJto1Kc1hTj0TwmB2LQPTWtHXO1DogJHpzah6P3HFrnWYJsVsy1ac3OE1TwBjVwmS0UH0SlvUn1lNLTlqaJm0tlPEYrudFvzV7NlCf1IwuiIO6HdJADjtWQKtrp1SRnky2RVCmgwMjo48VfkQEoTpqPpXaFqTuzA4flyjjPiBlR/aTyLWg15uBw2x+90caWweh0zhpXzEgGkqpEjq3MkWcJwF13jp3m4LEGSrRSk7UOS+A7vSUvWKfGEjdYZTc6j4TdWYPoVJSzogJcrMdFTLG/CUSpXQ+CwHEeit6zRBjlhZBH51rnBzUiRGjlo81Fw3i0DlLjxLVuhEnG8WbcQd1lD0DJoidWJBx/QpozsmcPNOCNO/Ge2lc7wkQZ6eeqEM5XnYlHD4iIJZOO++BpBU0Q3xU8T1hqPF+UvMAMtPYvnQc/j5gl6qnwwQhssWz9TCHVxNUOiezaUGfcXylPJSIRutElChNeWoBLg812kNxtiYZkKwduHzDjP8iJN2YbYgnPj88kIf2+nFRpBERRXeiS7Z2b0VZiR9PEEpcZYPT2xCE2fr1dkcEUutSmwhJVnWne1cmJ/sEPbZTNehDvgqAkxJJZuXdD2qpAWAyNzQwaUaWZJp+rhno+eBJYFTiRRVJu8FnZ/F6jlJTb1ktgGKMEAdsmQqZ6wB6u6I2s+waim3anndBa8e0z2q8U6Dc/rGgjLx2DBy9XtVZclFTDJmHz9BSvXYclDoQemUYy3sc1A5vt53fCxi86g+xBeZAcd0pVHf+HUbVZQUMep1NXcNov12HPe3egdIvfgHIJ3BUziAg94PNyqItgDozXEp5LtG/q80KoMtJE1exaEmd7n2jUPzwxtU77+PN+/IuJv7y7d/+Da9+9XfcQfz9r5kLWldG6LQkNh0M8yrITkarV1RTcufqZxUJQWvudfOxUPZ0OfY+c/up/Zvf/njBq9/9A28I//hPb2miWROaJTWanjTBwDZAsmRJkdQBTVwE108EWj7W/cq9qlgIcK0C65+/7nFmWGSeMFwB5BeLi9/+IJKqxnzXZJRZU0lM14sBUK3SAitrAq12QD9koxUL/tUDzf3/8nU++Llw4q19bhZ5+Pab32eXrlCIqso+iOBdllhetqbU0EbVOvSiIEoQ5vkzU/by/0r/xW+/EUvrBm1pxz5KNrfixIOtQQAlrbesq3NSIi5ur9z0+/Yb7PIuiQugBKEun5MSeze3S7emb78BpcM5FxZEORPgjJT5q1drU5xSQtvhS0x/StA6Mp6P8vamt+lX0hwLWp3HpxD9KREGJpyLspe/2H4vo6TdBr6hLl9K0Eoynokyf3v16HdGyWp8rpLpn2OdCW2CzkEJi4udBzxKrRR/iI34U6I81c9Cifd3e31El5KAYSRNCWKd2YenpsT8xZXPXz1KJXD5Uxj5UnZZxZ0q5Z6/MDXXLvJ+7/MoCXR46h8fSiTu4H2alNTE1iV9+w+925uA72NJ2TU4BhN9KMGeuN22NCklo2sMtvzx7+59Mqt3aUmp7HeSw8uP0hi49m+alMRoaPr6Uv4mH5gdl5So+gx4hNY+JcptLXVKtbNxkcjfLQ4EsaIkDTtJStCHbglIkxKq61KGF72gzOpd9yhpOYq9jNTPwgO7mT5lzevZI+Qvjrnnryj1Ufy0vM7t2hrEcLyuaqpp6Q6l4uJq0TsSxIqS9ngjFUzcHpXcG6REaTkJnGp7yQolSvevjgexoiTQijLRh7nL8dayqULx9aNBSlSXJmPato90e38Vom3YUJrtCN4NmCv2t7Be9y+/L+CmxQW7raaeY1lmDcW4Tal1Ii2yfjNm5pU3VknKAJ9fw2apFThLuzhVyt5dvhcuymtKd84g9Jsx96H8jnKVr5lyQODdA1x/GMP42p1/aDqpU+bzN+Gju6HsRGgxof+uP/5Ictdjphxi7n0OoXgJ1w8uZd1OlxLJ4u5Yxbp9+4ayFWGGEj5+KvQvIdd3VUB4XQCGDmO36YT6aslkSpRXNyHzqqctSiH8gCXNsNfwntY/heX8SH+MgND/XH5wy+Z63Wo6lPnFq2hG9xalFr5bAtdvoPD5GpbL/mE8BnjIwfinsWsfgDVPkRJvrvIRexbblPPQ7lXw8ECzZ3llRRbevf/wvghw/bngzfma7dQoe70/RO88bShRnIVuSjDndtRXv+aYqAXUH692V2qmRMnMuRg9xC1KNYIX2c5IhJtti8X+aseKRisVSiSrKYGI2qaccg3kQf9hvemDkUmDsnd7F3NAdYtSnnNRks3OFlLLSYFycROhhXysbcroiyB8wnNDGtQSp+z9mI8N+YhycGC++WBOWfei0d3jAuWmkDBl7+CAx1FtUUqtYLMApUMre1eUgDWHbYshNa2Vawyl3PeXiShHvb3jDIXN7HkiXSf4NqlyYMH/khL0eqneyGQyxrTLPpj++Ccjw6nsb37+I28gv/u37OrHST0beFu2U5oHTv+tc6xtDCqCIFQmDWGpP/97ReBT5S8/m5xBCMLPv7aXP9XqreDbzHY2uG5aUwJxNzph5XIp3hzbo+aco3IFwbSVY1tm8G1S8M4J22N46G6NJA8qidQ+CFc/rupYkGU10rLNRwGFq30Ob1S5M1K5FRIXJd4v7smSEjRBq3ZjO4tstSTNQzNCiMGr7XYpSSubACXNrG4LyShBb9HMZMZdk7JNGTxWSTuMqtoMbE53R52hYXBT9u5WgwFsDzVpqIC7r1S8wLbt2EkwJTGyQzMw1+5Tclvrr27XZgCjNDvMj8yMu/F6SGsdtFL3aHu5udvk6nkhyd/0NlGhlKTFzH8YNPgpxVGgNzNbaRy0XynxoRR4xgrw6upm+12UUhpYLMOW4q6i2hor0DuBgYAzPLSGaY9SmcSnxNudQR1W+3RpI0cGMRcIPB4RCfRtAqukQasRGMguJUqxR7dwsdi1y1m51NuaaETYr2I31A1lNbC5RFmmNY8ccNVn/hLmWqzxWLx6tX+725KAbXHsKLFF6QRnCNeiOd4n2USsXotDmb+98hlmXdo+PH3fLcpmzPW1PrO00G1Ep+zld12uloHx77e+RVmK7QyzT1lpkYhzXsHzV0lSojSLvQ33PqWynEALTdm7CPTwSJISrHpsj589SpSWK3XDUWJvcRf87kQpjfjn1vhQzu3wlHi7ODQlkCAlSs1scpS0YBphcyziHw7PXyVJqXbiL63zoVRC+vvg1f39kfcmSAkKhyeMj++W2AlH+er26GuTpBQGiVISb873MCUs7qXgq+u7EqNEqc2x1t7P29CcH6PE/E0IxiQpQeTx6faj1N3e6gHKvL/D7r4SpKy1Yy+28F9pAdPaIUoIPyWQICXXwWC+lAJbpRtEubgPP9maGCVKE56DwXzXIKgzMWANAi4OOOzuKzFKqHAdsuJLKQ0cX0rs+fQhDykpSpTbHD7AQWuDhJIfZe8uf9Bh1yeghChB4TuV0H+dFxv53KPMX0Sea00sLbMGVzgBa/acwQ4lLq4uooeeECXKPK75JIiS1j/ao/WXvVdHnZL9lBAlOC2+LdWCVpk2DbKhhNtXUV2ulg8mQgnqkHOrsSBKcaSuKGFxF7HS2QSTDGWFa5EXCV79TYzskjJ/fxX7HclQ5uZ8+4wFrKUlbCD7r79klPmg9VehlAylzX06R+CuDND6j697eHXD5Q2TDOV/xt6aZneHje0RfuaaR6vZ//rqfnHF6RSQgF/Bxdvfx61gsXDt6XK8/GGzegZkVVWBwJ/ffv0Vp77+01veIL766m3sthL6r3e0zrmgC7rWqgL+96/+8opX//O/3EH8388ckyy7WvOLzA3AbtM8XfuBexcj3j1hEPS/pnBMMcpDNqvKJkQRBlyb4ZEEah+U4k+OHBCYU+YGILBOK+glzgNC+XcXy3LtOhEgJF3mIwItd1gQahO+d3DvFKeU0jgzAD03AM2bK0GpxbVNAPeuf2onlS2B0fXOJKsNdUAdcW0Wx7uDI3fFEBSw3tREx1wFDspUO5eFh1ibpLWDLKgNBTZ+7JiZcuxkz7ezajW13YBBa7cUkFdnirKR+2x8TK69gKVhWvt0oyQ4g3qnpW7Ze7NG7HqOZ19naZjenuvMipcenX8HyiR2T51jdzGpO0h3W+edpAM7tnEQf3cx0pjGdhyOJ4oZs1sQlxLR5NyfN4bAnMc7hSomJaIQ7D6ZmhArs/3TuEMoHiWCMDrH8UEIlWmcLzcWJZLaGVLSfTNNzYgnIzHFoURi8m0MziGWi6zI7WYMSpCM6flOu0KwRpGng6NTgjqon/VIL4oZ1diLSokg1usnbid3BXI94tFpUffDI1rJObwT7AkEcjfacZzRKBGdknXO84RX8SCVkhDBdTkKJYLUnFSfxNmQbJPTTvhjKiNQAhFGmSdzzifI2fBnp4WmRFCNkfAkEtITolKfSOEMvpCUtMKpDbuHFxeeXCCZo6we5osPRwlEadaf3CHD7MS/1qgSdHj7lkJQ0m67PCgJZ24k/QVQbQ8F+RjnUUqaV0VjajyVY3f3BMSqdypHOI9RAurZUjfc2dPnEa0W7c68cXA3hEOUbIWvNhgN9CfTfPiLRlNvlgZ68OryAzvFgaQqo1kGnuhJ9Y8ERDPn84qyv7Wvd9mXkqWibHdnAzuB3U9OIgSUtfmsbrL5zr1k8aFkd0l6a1LKqtITLo978lJmUhrYmgSPc+BjStdjQ6xW5qVmNij1n7Jo/FXLmY8GjYqle6jLGXfR+8n19lA12zE6o7ZdJV9CafQTbfkkVavVJ51Op5m1VZlJaugS+1SrlW6905lMWjb945eK6MlLMtE2G61BezKdDYedWWc4nM2m9eYg61QUyUvkc8czCTFUQpNP1HVN71qapuuiKu+W2OegdVmk5XJZSM8dpRSVgB/eF6AXyuejF8rnI+ZteO44pC5Q2uYJj7aOJf42DqqlEXco6Ta1mCtwByENOBYzr6ORJiaUP3OHD6LI24eEhzdp5nm4/o6bEsm4eM3pIVv8KVXKcgKU/eLr78dcsYTi92lTRu5FsP4Itc5hebovlglcfgA2ChIz52L6lDlSjvjM9U8P8DAuf4T+JdOY0hU/0RL+Ovf+IU5ksZB7SJvy4eNnnyOXD+qyCJ/HuSJ4i1QKtBn4eA1Q+NwvFzDOmpn+u4/pUl5/9913Hy4j6YH0X78ujscFKLunLJQRxjQNMffumnYy+9ECc/WJRiLltPz0/n0hF0lw/f11/1MfliusEMrFHP238OYBMFpIS/U/v0+9XJbH+8trDi9yuX5DHi7X5gqU+wT65Ydi/8M41vIZKJdPUMdGfQEWypBbz1Rj7vL9hw9v4KGQK+6ewhQ2wBO0JDGc6OCR4ckyMW1WEGOPbD1Jyh3xD2t9CZT8eqFMIvgErPUkopGutY6FjzHrxUQF/U/pLkV4GiP+X9Ik54te9KIXvehFL3pq+n/p6qjBYDWkJQAAAABJRU5ErkJggg==

 

This is a diagram that represents this situation

 Mar 25, 2020
 #2
avatar+128408 
+1

The  lagest   possible rectangle will be  a  square with  a diagonal of 2

 

The side of this square  =   2/√2

 

So......the area of this square =  (2/√2)^2 =  4/2  =  2 units^2

 

 

cool cool cool

 Mar 25, 2020
 #3
avatar+2094 
-1

Awesome, Chris!

CalTheGreat  Mar 25, 2020

0 Online Users