Maths-
General
Easy
Question
In
and
prove that ![QM squared equals PM cross times MR.](data:image/png;base64,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)
The correct answer is: Hence proved.
Solution :-
Aim :- Prove that ![Q M squared equals P M cross times M R](data:image/png;base64,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)
Hint :- using inverse of pythagoras theorem, we get right angle at Q,
Now using angles prove the similarity of QMR and PMQ triangles. And find the
ratios to get the desired property
Explanation(proof ) :-
Given , ![P R squared minus P Q squared equals Q R squared not stretchy rightwards double arrow P R squared equals P Q squared plus Q R squared](data:image/png;base64,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)
Here ,PR is hypotenuse and angle Q is right angle.
Then ![straight angle P equals 90 minus straight angle R](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAAAOCAYAAAAohuLlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAj9JREFUeNrtmEFEhEEUx8dKVhJJkg6RTh26JNlDsiQrSWKlc3TqsIduSZJIp3SIJCtJZHVKImslHSLp0CGRTh32sockK7G9x//jM81s84359hP753eY+Wa9mfe+ee/tJ4S9xkRd4j/4b4c41jwrExXwQZwQScf2R4hr2PokckSPYl0L9noLdjEXtUz894Y9nxPttob4wCViSPGsl3jwjRuJUeKV6HP4Rj4Sg0SMaCDmiCeiQ1qbJyZ94wnMRakg/mOtE5s2hg6qGGJNEUeKeXbmoqPD3mluUVo6FI+3Feu2iNmIAmXjvxkiG9TQ4R+GWCuaoGwQC44O/K2Z51t27xvnNHUhiWe1lq3/VolMEEM5A0MC9WlSmuN8+0y0SfMVA1R6IQYU892oX55KSMOyeK5Y40DZ+q9Fk961b+upoSGBoHT6xuzUG8cNRho1cAT7i6EW8a36MriBQloXpmz9x3U4hTOlTQw1BDQUg4Mq+A0HaU0KnstusIDOqYw3sle6WdWCVdbM29521/7zGDY1dBbAkMC6QoDDuHQMK45W11NRkwbjNUiDLvyXMOkCG9HbBzEk0GFlRXRK4ib760RK0/qH2WC49N8larH27bywMCTQJs9HGCz+P9LlG08Te4p12RBbd9f+S6Dd/6Um/GG0MSSQn8drEJQ8AuGlOA7QsqILFUgrGaQlXr9EXIW0r7D8l1d9UCgY1hEP+XNJCW9W2BrFXrkYv2Mf/Zq1rcS+77MUfz1oDmlfYfkvgbRa13/SDxMExX2eruTKAAAAxXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyMjIwOzwvbWk+PG1pPlA8L21pPjxtbz49PC9tbz48bW4+OTA8L21uPjxtbz4mI3gyMjEyOzwvbW8+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDIyMjA7PC9taT48bWk+UjwvbWk+PC9tYXRoPmJGlxAAAAAASUVORK5CYII=)
![straight angle P equals 90 minus straight angle R text So we get end text straight angle P equals straight angle M Q R](data:image/png;base64,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)
We know ![straight angle M equals straight angle M equals 90 left parenthesis text degrees end text right parenthesis](data:image/png;base64,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)
By AA similarity
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU0AAAD0CAYAAAAfQnTNAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAErCSURBVHhe7d0JvG9jvT9wN+7/3m7d6nYbhAxRKkWDFJG6IiRDN6FQJEJERSFDFKnMtzKEkqlSKVPmWSRzRUJznSMhKtNh/X/v5+zv9pzVb++z9/7tvc8evp9zntdv/35rrWeNz2d952e+RCIxudE0zfyd9u+d9vROe1anPeeJJ554fqct3Pl70c7nEp22VKct3Wkvf+SRR17Z+Xzlww8//PK+Zc/r6yoxFHQu2C7ZsmWbfK1DiPt0Pg/ufH6r83lWp130+OOP/6jzeUOn/bzz912d9odOu6fz/YHO5yOddfvR+a3pW3ZLpx3RaV33k23O5i2VSCQSiSFi2KTZYdrmicdnt0QikZhuGDJpIsv47CfNNm/6nlyaSCSmMIZEmojyscceY/8o7bFHH2seffTR5qGHHmoefvjh8lus98SsZM1EIjF1MWRJM4hxxowZzTXXXNNcceUVzWWXXdZce+21zW9/89vm0UcenU2afRJpIpFITEUMmTRnzZrV/OMf/2jOOuusZquttmre+973Nu9///ub7bffvvnUpz7VHHXkUc31119f1kniTCQSUxVDJk3q+f3339986Utfal70ohc1z3jGM5qVVlqpefe7392sscYazatf/epCnj//+c/7pdJEYqIgX+SJ0cKwHEHsmGeeeWaz+uqrN4ssskhz+OGHN7/73e+a73//+82qq67avPGNb2yOPvroYudMJCYKOC299GlLYUKqWyIxHAyZNANU8K233rp5yUte0pxyyinlt9/+9rfNtttu27z4xS9udt555+Zvf/tb+T2RmFeg7fQTYudj1mOzkjQTo4Jhk+ZNN93UbLPNNoU0Tz755PLbPXffU4h0oYUWKuT54IMPlt8TiXkB5PjXv/51Dvu635I0E6OBYZPmlVde2Wy44YbN4osv3hxwwAHNbbfd1px15lnN8ssv3yy55JLN5z73ufKwJhLzClTxmTNnNvfdd18hSvAZ0meSZqIXDJs0r7jiikKaCy64YPOa17ymeec739msttpqzRJLLFE86hdddFGxfSYS8wqI8JFHHinPYZBiTZLtlkgMB8NyBMGPf/zjZsstt2wWW2yxZt1112323HPPZq+99mr222+/5rzzzmvuvffefBATExY1WUZLJIaDYZPmLbfc0uy4447FpnnggQc2d9xxR3PXXXcVZ1Cq5YlEYqpj2Oo50hTQjjS//vWvFzJlK5rDW5lIJBJTFMMmTamT7JhsmN/4xjf6fk0kEonpgWGTJkfP2muvXcKLeMrvvvvu/mIeWeEokUhMdQyJNKndEbpBPf/Yxz7WvPa1r20+/vGP9+ebq3xUsi4en71eIpFITEUMiTQRZpSA4x0///zzm09+8pPFEXT11VeXDCAhHtapwzwSiURiqmHI6jnCRIiIUdDw7bff3vzqV78qmRfhBIoA4kQikZiqGLJ6DkixliL9jUgzmD2RSEwXzJU0EWO0Gr4rFfejH/2o+e53v1tKwv3973/vW5pIJBJTE0NWz9sgdf7hD39oPv3pTzfLLrtss+uuuzaXXnppIdI2wSYSicRUwYhJk+1SFtAuu+zS/Pu//3sJQVKQWG1NTqEaYfNMJBKJyY6eJE3pk8KP5p9//ma++eZrnvOc55QYTl71c889t/n9738/2zHUx5fd1PxEIpGYTBgxaYrJvPnmm0sdTYRZt2c/+9kla0gV95/+9Kdz2DqRaEqeiURismLEpEkFl1K50UYbNU95ylOKio4sSZvmD3rWs55VbJ0f+chHmgsvvLCZOWNm8bIjzAxNSiQSkxUjJk0EeNVVVzXvec97mqc//enNyiuv3Oy///6lRJyCxFR2ZGouoTXXXLPZd999y9S/soeSOBOJxGRFTzZNVdu322675mlPe1rzP//zP80Pf/jD5s477ywzVm6wwQbNC17wgqKuI1DzB22++ebNiSeeWGydbfW8fE+NPZFITHD07AhSW/OpT31q8+Y3v7k555xzyrJ77rmnOILMj66EHLX9X/7lX5oFFligTPt75JFHlhz2egK2mC0QwmEULZFIJCYKenIE3XDDDc373ve+YsdEnr4DtZvz5yc/+Unz5S9/udl0001LSBKp89/+7d+apZZaqmyHZKVhUvXZSPXZJsxoiUQiMRHQk6T5y1/+stlhhx2a//qv/2re9a53lbJxNcEhTqq4303t+9KXvrQ/PMkcQ2uttVbz2c9+tkilf/7zn/+JKOuWSCQSEwE9SZq33nprsWnylnP2IL9uBKfIx3XXXVdsnRtvvHFxDiFOjiLFjIUnHXXUUSU8qZ4yI0kzkUhMNIyYNKnUiJCa/Z//+Z/N+uuv31xyySV9S+cE0kOyVHAedNLpcsstV8iWrZPKbmZLqZiI93e/+90cWUVt0kwiTSQS8wo9qedKw1G7ec9f//rXN2eccUbf0jmB4MLJg2yp9ccee2yz3nrrNc997nMLcYrzfN7zntesuuqqzUEHHdT87Gc/K1JnkGMQJXspAvYZv7VbIpFIjBVGhTQRHknxO9/5Tt/SOYHIkGUQJ8L705/+VAp8iO3keUe8VHafguJJsF/72tcKwUZGke30oyVpJhKJeYGe1PMrrrii2Cj/3//7f83rXve65nvf+15X0vJbSIdtUMXNasmRtOiiixapE3lS+ZGpOdV52f/4xz8WlT3IVxuIOBOJRGKsMGLSfOihh5pTTjmledOb3tRPmj/4wQ/6lg4diE+8puwiU2jIJlp44YWb//iP/yhxnVR29tLjjjuuOIqUngPkOFCIUiKRSIwVRkyaPOJsmMKG5kaa3cis/Z398je/+U1zwQUXNPvss0/zile8ojiI9C0O9A1veEPziU98orn44oubBx98sEidjiH6rlsikUiMFXoiTZ7uddddt5802TS7kVY3QhuI3EiPv/jFL5qvfOUrzWabbda86lWvKqo6uyn1nfNIwPyNN97YPPDAA3Oo/P4OtT2RSCTGAiMmTZKeECOFh6VRIs3TTjut39lTE+VAbSDoY+bMmcVRxJNuHxHbSfrkqeeAOvPMM8u863Vfta0zkUgkRhs9OYLMDxRxmkjTXEGBmhwHat0Q0qLlpE4zX3I4qdu5+OKLF4ImdbJ5knK//e1vF8lUOmbdZxJnIpEYC/Sknp911lnNOuus0x+cznseCGIcrHVDt2UcRSZuO+CAA4qjKMKTnvnMZzavfvWrS3m6E044oRQQQbQQpDnQfhKJRGIkGDFpctwo87bKKqsU0kRm5gcKBGEN1rrB7wNJiUiRF10BkBe+8IWFODWZRSuuuGLzqU99qkilf/nLX0ofkBJnIpEYTYyYNCPkSCxlSJqnn35639LeSDPU80C9PucPW+duu+3WvOUtb+m3dWry2D/4wQ82J510UiHYsK8G9BFkmkgkEiNBT46g888/v3izkSZJj2NmPMCeKthdiBOSXHLJJUv1eMfx3//93yUV89BDDy0edjbRCE1CmG1CTiQSieFgxKTJdqhepmrs8scV4bj++uvHjZAQIOcPWyeJl12Tyi78iZOI1Pm2t72t2XPPPcscRUrPpZSZSCR6RU+Spukt3vGOd5Tgc97tH//4x31LxxfIU1D83nvv3ay22mqFxKnr//qv/9osvfTSZfI3sZ2KgISjKJFIJEaCnhxBxx9/fFHLhRzJDEJc44ki1frf+USGv/71r0sI0k477dSssMIKZUbMIE9e9j322KNInUKU6qk2EolEYqgYFdJETv/7v/9bHDRjDQQZjbpd2qzHmycen02cKiL94Q9/KBWSSMGkTup6ZBQh9913370c69yIM/aTSCQSgRGTJnI65phjitfcxGnbb799sWmONwqxdQhTq2ezlCkk/Ojwww8vGUXPf/7zi9QpxpPtU9gS88JA6joytkxL4kwkEoFRIU2ea6XdLr/88r6l44eQBtsNeMpnzJhRVPLPfe5zzRprrFFiOpEnEuX5l+Nu2g6Scw192J6nPvpLJBKJEZOmOE255uY7F+qz8sorN2effXbf0vFDmygHApKXsYQozccedTuFK1HXxZiavkNx5JA+gziTNBOJRGDEpEkCUwNTEWIqrzxwZdvGGzVp1q0beNkVGRHbyavuuNk7mRde/OIXNxtssEGZ4K0dGD9Qf4lEYvphxKQpYJzktvrqqxcni2LE4xXcXqNNlmyRCM9nN7IjcbK9mhlziy22KIVGSMqkTlMRq9u57777loLH+kmbZiKRqDFi0mQDlAeuTJuQHnUvB5ojaCxRE6Y2N9IMsHWaGVMEwHvf+96isiNOarv52YUtMT/cdNNN5QVRI/pPJBLTDz2RpoIdbJmycEzJW5eGmxcYjCQHgirwVPZtttmmeclLXlLSML0EBOyTnk3BIf5UEZAA0hwKMScSiamHnhxB3/zmN0vRDCTz2te+do4qR5MFSI8kKTCeZPmBD3ygWWqppYrK7rzEoMplN/nbvffe2+8kQpipuicS0w89kSaSQZrCeMQ9XnXlVX1LJw+QnoYA5afLpxcY//a3v72/bidnEeJk6zTFx/33zZ7cLSXNRGL6oSfSVChjpZVWKlk3CmPcdtttfUsnDwphPvpY8+gjs+dSB5lCKijJpxeHKk2U5Ck8SeaTKThUreeNTyQS0ws92TQ5UZCKQPEDDzyw+dWvftW3dPIAaUYaZsBvQqoEvfOyC9xfZpll+u2dphVWVYnjywyaobIHbJ8SaCIxNdETafKeTwXSHAicPffcc09z7bXXNkcccUSz5pprlvAqKrssKJED+++/fykAgmStX0iY2l6RcCKRmDoYMWlGGiUHEPWV2nrZZZf1LZ1aUAbvt7/9bYkOCC/7U57ylBI14G/n7qUh1z3Ck4I84++UPBOJqYGebJqnnnpqme4CeYjTrCdWm4pgw7z66qtLHjuVXRYRqVNDnmygroEqS0GYUBNoIpGY3BgxaZKo5Jorv4Y01auc6qSJ/NgvOYrkqfOmU9EXXnjhIm1rHGOHHHJIc8MNN5Q8dhJ5hiYlElMHPdk0I05zgQUWaJZddtl5Htw+nkCGv/vd74pKvtdee5WXhusgTEmc5/rrr9985jOfKYHxyJOzKZFITH6MmDQ5PtgwFezgHJkupNlNYhRqdfTRR5e6nWp1zj///CW2k8qukMmxxx5bCHYigJmgOKr6TAaDScCWpYScSMyJEZMmlVNRC44RpDkd1POBgHxmzpzZXHTRRUXqXHvttZuXvexlJX6Vl135vM9//vMl190UxPMKQZSFLP1rFW5uI0kzkfhn9CRpIgHFLqaLTbNGN0LxHSmed955zac//emiorN3eqkoCOJasQPzxDNvzFMkFyYSI0JPpMmTPF1Js0abQBHnHXfcUbKKtt122+ZFL3pRsXcKiuco2myzzUouuxhQsZ3jAcdnXzSEfvVcUH913IGyrE8i7ZdMu6yXSExH9KSeK5umoC9JajqEHHVDkJGXiBbwu1x26ZZUcyo677rSc8985jNLoDxbp8B4caBjjfvvv79MsaxwtOIkoh+kj3Yjwz/+8Y9lPREAbLE5c2ci8SR6Ik1hN1tuuWVxepA0TRkx3dAmTVIZ+E2znPfc1MKulQyqpz71qaUpeLzbbrs1Z511ViEy67cxWlLeL3/5y2Iy8JI74YQTCqE7Xn3X/fv95JNPLhPlCZ2SDYVwR+MYEompgJ7UcxOpbbLJJsXZgQDOOOOMvqXTB8ikrcbWLdZhw+RlN52GGqSkTuFJqsUL2yKNqiivbmdNZoh0NIjzxhtvbDbccMPinNpoo41K5IOwKbbNJ2Y9eZznn39+iQIQNoU4vRi9IGc9Nj5mhERiomPEpGkwm0vnox/9aJljZ5111imzPgZi0EebqmifZ7cWQD5UXxL5rrvuWsrNkThVUOIwUvRYgRCFQhBaSKqBdr/1srnhlltuKeFhyvgpPELqVWwEkHJ8HnbYYaVyPcfVDjvs0PzsZz8ry5gQhrO/RGKqomfS/PjHP14GoelxzSMeGOngnmxon+dgLUDdRUacQe985ztLlfiYaoPEvssuu5QXUHuajcH6nBuEhyHKcEoxp1x+2eXNww89uQ9poswFCy64YCFxL0Q2VxjI/plITDeMmDRJHpdeemkpkUZ6WWGFFeZwBI10cE82tM9zsNYG7/kZ3z+jv24n8lQIhJd98803L6XnqOzWqzFYnwMBSW+33XZFukWIiy66aMlYuuvOu8ryB/76QHPe+ecV6VJOveU1aY6GiSCRmAoYMWlGEWL2ON5zg752BNUDeyoPtvZ5DtZq+M52qQr8zTffXCpGsTnKKOJY8yJS9JhKfdJJJ5Wye7zYoUq3+2z338bPf/7zIsGSNmkFiy22WLP88suXsCi49ee3NjvsuEPRHNg0X/GKVzQ777xz2Q7m1n8iMV0wYtKkOnL8mBbCICdpxgBMzB016bF1kiaFJ/FwC0eiIlPZhSeZZhiBmWqjW7V4phIEHE6jbmAn3XvvvZvPfvazzaGHHlrIc/HFF2++8IUvlGB7WsPOO+1cpjARCrX+eusXkg2bZkqaicRsjJg0DXQSUsRpTufg9l5Qk5y/qcPnnHNOs8cee5TYV/ZH5EmlVreT910mlimIA+4FcwnSHIg4OYI+9rGPlX7NT8+eSpIlde6+++5FVdc3D7/wqPXWXa84q1LSTCTmxIhJ08BUN5I0wvtLGpqMs1HOSyAihBckVxPTnXfeWaTAt73tbUVlR56m2mAGYQNVNf/2228vZhLbB1nW/dUQqO4FZ1tpnoj3rW99a/GSk2ppDELIxGny4NMc2DRJqIlE4kn0RJoCsj/ykY8U+xspiIqXGDpcw1pCjPhMCJWdI4ha7aXEQSS+U1zs0ksvXa69a37fffeV9fUxkEQoe+tDH/pQib20zd13312m8CDN6pPtVBA+uympk5fd+rSJRCLxJEZMmgao/GqDUMA0z6wBnhg6aknT390kRLZjKjNPOjV6xRVXLKTJy87Dvd5665Uph73AxHZ26wPcG3O6f/jDHy4SpfvHhkraRMgkVwH49/z5nqLCMweYllnqZSKReBI9kaY4TYOQBMT+FU6DxNAQRNlNOoxlIT1Sw5HniSeeWIqkLLTQQsXWSW1/4xvf2HziE58odkrpkjVx2vbBBx4s9maq/gYbbFBsmvD73/+++eQnP1nK2d1x5x1F0j3/vPNLDdAowsIxZN+JRGI2elLPeV132mmnkgrIVvaTn/ykb+nswVq3xNDRvnZ1I3lKdfSyQmrskRxxpE8hRFRrkqT6ntaHmXfPLAWi3SPbqfsJVPFLLrmkFOdAjAiaE4iEiYhlednuwQcf7O8rkZju6Jk0eWQ5gmSyhAQD9UDPATc8tK9dtAA7qHRMIUhIUDA6iVPFeCFKKip99atfbe6/9/6yvntFdf/z3X8u6ndIjvrUlxb9C2nimWfftA/fmRASicRs9ESa1DtqufxpXt3ae14P9hiQiaGhfe0015sk2I/OJZXFw8Ej+F3cpfnnqeziZiUdHH7Y4UWKJHXavg39BmI/3TDYskRiumHUSNP850mao4P2tdNc73AaRQtQ2a+88soi9b/yla8s9kgVlLzIFDw+/PDDi+mkncuOhDV9mfrCZ3zX7M++oazT93ciMZ3RE2kqUCvtziBNSXP00L520QqZzeorQVfNV2EZFVuqpTnZ11prrRKSJBSMym6CN7bniy+6uJk5Y2ZZF4IIEWYpD9f5zxkUZDlQZfdEYjqjZ0lTcDtJU9hKplGODQqxBXkNwmHuCVWc1Ln//vsXZ457IzyJwwiZHn/88YVcEaf1A9G/3/p/T75MJP4JPZGmjKBQz2WQTMcixBMRCJEWoFTfu/73XaXeKVunIPZ3vOMdzZe//OXm+uuuLyXqAu5nqP+JRGJg9ESavKvi/KiBPLZ1Pc3EvAXJ8fbbbm8223SzQppqdUrDFFO7xRZbFOfRySedXILXgzzd0yTNRGJw9ESawlJkqUTldvGDiXkPDh9edRWNllhiiRKGtNxyy5VpNsRyKjRsHiC1UKViChVzL8VjzuGhTyQS/4RRsWkKrjYYs2DHvIf7ojiHLB/3ROKB6vDSMHnQpVNKuVTsY7/99mve/OY3N2uvvXb52zoKhdQ58IlEYk70RJrhPRfcrmitQZcYf5AOw+PNZKJeJsnyWc96VvP617++FDhuT8PLHq2KkcIczCsC5FV1dz9VQSJ1BmoCLep7avCJaYyeSZOkycGw2mqrlQyVxPjCfUCYmmpH8s/dC2Fgps8wfYUZJWuoniSnnHddPCdbpxefT0VAzDD6jW98o9QSUMSjhv3kzJSJ6Yye1XPSChVQBR1zZCfGDyRAJEadNvWvydgUFZYRJK1SrUySo1Jw6mQWwutIpV5uMZ0vezSpdJWVV2le/vKXl3uJSP3GXn3D9Tf056VD7C/gGLq1RGKqYlRI08Dbaqut5ijYkRgfIDOxmd/85jeLM4533DQWMoPMEqqAsamB99lnn2LrVMFdRSSEijS33Xbb5twfnttcc/U1Rbpk40S47NScSEr/MbuQOss86R3UpNgmy2iJxFTFqNg02cTMa3PBBRf0LU2MF9gqzz777OIJZ8P0AjOTpVhMhKeEnOB2GULWsWyZZZYp0ig1XkJCZAhR21U5ev/7319snaGuW4+aT6VnM63RjTC1RGKqoifS5EwQp0mdUwE85wgaexRC6uMkZHfZZZeVaSxIlF5epq1wH9g3SYekSiXkLBPgriFDkqhpLbz4wP2Mz/C+K/rBLirGEyGrx6nau5qdNdqEWY4xkZii6FnSNChJLTmx2tgDGckHB2q5Sdh23HHHZpFFFimxmKusskqJv2S/BLZHKZNHH310s/rqqxfik4tOelRpX3hRN4JjtxSWROXnFKKmu8dejshWzU7LlZATGB82ziTMxHTAiEnTwBLzJ7uE51VMYJLm2KGfMPs4iZRv4jWqNulxpZVWKrNYcggV8lK1SMGNzue9995bUlzN4yS0SCol++UDDzwwu7Mu8FK89y/3Nj+95afNV77ylUK6pE62Tiq/+qlUfSq7/gPlOPuk1kRiKqIn0pR1ElP4Kg13+umn9y1NjDo6ZBnEiTCFFpkviASowhRVu46tRFylelGf5Eci5DW3HqKLIPZuiLjPgP2p4K70nBoDJE5EzdOuCMhhhx3W3Hjjjf0e9kRiKmPEpGmAmCOI99zATZvm2AMRcsQgTI43sZg85J/+9KdLJEORMPskvfgb+dWSn7jLcPwEobZhG6mY9XZ+Mwc6m+ZGG21Ukhncd06ml73sZaVwi6kzHF/0n0hMRfRk02QvQ5rmp6Ee1tNdJEaOILz4Oz7ZEE86+aQSi0naEzb07ne/u0QttKU869f1MH1aR/N3fI/lNWI5BAEDyZQqLrTs4IMPLrnspE1VrqjsjuvAAw8ss1yyq7aPKZGYCuiJNM0RtPPOO/cHt+d0r6ODIC0NUSE/xYNVJuLBRlLqYyosbJI0nvJ6u/i7lhQhlgXa37uhrNNajRRKvReexKYtLpRHHpELbZLrfsghh5R1QtLVT+zPZ03GicRkQk+kSSUUpyk20LQKV199dd/SRC8Iggmb5Iw/dSTME08qc5QjJlKdl5RwozrgPFqg/nu0QYpE1ldccUXxznt5vvSlLy3kycbNyy5wnp2bhByoCXQsjy+RGCuM3Kb5+KwiSZB2YgbErKc5ekAoCAY5CV7n8Q5Cet/73ldUcqRlnVh/PIgoiDyOL8BZxLZKZWdnjZhQtlcFQ6j0ys/Vc6gHgSYSkwkjJk1qo5AjsyBmwY7RB0IhRd5xxx0ls4fdWBOLyfsd+eBBYHUbE3S6tT/FOmpbacDzwAmkPCCVnflAKBpTgsD79dZbr4Qu3Xzzzf1efudYE28iMRkwckmzM4DUZBQkLWiaR5Wqlhgd8EAL4yHJmxiN3Vis5CmnnNLcfffdZZ02WUYbC+jXMT36yKNdiS72y1HEts3LLjBeOibpWJ67CAvPybHHHltCoMbyeBOJsUJPNk0ZQWL3kCYvbpLm6IG6qy4mJwsJkwNIts9f//rXsjwIp1sbC+iXU4ekSUWfG+SxX3zxxWWCN7ZYEid13SdTjmmFTQBXB8YnEpMBPUmaEaeZNs3e0CY7jhMZO0E2Zvr86le/OmgGz3hhOKSMZJE/r7/q8NR0jix58EsttVQpDOI8b7311jnOrexjbLg/kegZPZHmbbfdVuaYIWnKFMl5z0eG2rbHjslxouK64HFqubnM65kjJxPcewH1bJnmJhIUT11XBIQEjTzZxVWL59jK5yUx0dEzaSoZxhFEGqrTKOPhz0Ewd5RYzA5pshnKqmELdE1JZiZHYzueTHAupMw6jdPzQqL0QnjXu97VPP/5zy/ESWX3N/PDF7/4xUKu+bwkJjJ6Vs9JmiQGxWuFxgRqwsxBMDiQjIBxpCLuVVENqYl77LFHybqabNfQsXo+wuOOQAMyhRQWcW7y1mU1IU7Vl5Zddtnmwx/+cMlzlzgR0nciMZHQkyMogtuRpgFAxYrBHQM9WmJgIBV53VIQVS2KuX0Qh9AiEmghoUmImjQ9ByGFcgAJUUOSAuGFKIlD1ZQZlKZpbqPIdgrk85SY1+iZNE2shjQVrK0dQfFw50M+ONj7qN/slkKLONVMeHbCCScUtR3a17JuEx2DHaeq82qCchSxa6oLSmVXiGTJJZdsNt1001LTU1B8FBApbdbsz8lw/omph55IkyQUE6sJObr88sv7liZpthED3rUgafk7YjFVv5eCyEGi3JupKoRzta9bfT2jTXa4DmqAmpRP2boNNtig2DhVT/Jcmd+IKi8DKoorB6bKNUhMLvREmgZ2PbFaXbCjHtj5YD9JmkBlpXabNoLzA2GSsHwqLMyOWaN9Les22VGfA/JkF//Qhz5UguIRJ1unWNWNN964Oeigg0oscFtlTyTGEz2RprQ5we1IU2aQ/OIYBPXArgdGYra3nEpOslp11VWLRKU6kGvp9/p6+RvJavX1jDbVEOm5HIzy2IUkxTQdbL0yijiKmIZI6kPFVLxWiXmDnkhT4LI0P9PG7r333nOExkz1wV1jOOdJNQ8bpphF6YVqkZI4SZhhxwT9WX8gwtSmIkjhisGY4E3BZUTpxYw4EagY1j333LNUeSKdumZzuxZT9Volxh89O4IiI+i9731vKT473YDQ2NqojAYvkus6QDs/yds2IZnYSx5j6ievsepAwrcC9fau83Qe8DFNh2lVmC9cM6YMjiJ1Ow844IDm0ksv7U8vBderfd2m+3VMjB56tmlSKTkwZARNx8rtSJN3V671QKQZ32fOnFkkJ5PQiU0Uo6jMW12HNAf37OvluroWoCoSWyaC5ChiyiB1IlAzZbqGPPBeSLGNPp6Y9aREntc1MVpI0uwRBmKp/jOIiuh3udXiWGXDkMxl/Gy44YZFSooak53hnQO7BdfDs+Zl5KVDJd93333LZHKuIalTPjuVXYETCQJCmdyTxx6dXWCklLPrI828vole0TNpCm5XVMKUrtN1jqC5DUSkKAsGYUYQt2QAamfklOuDdBUS1nQf3N3OH3EiRM+dECQRGwsvvHAhTi9umVTiPU3DIcVXAL34zkRiNDEqkuZ0Js0gu8GITmiRWENOHyqlilCq+9SEqQnaZvfUX+JJ4qyvcYBkz4YuDMl87l5Gri2Th+pQpgNRt9O1TyRGE6Oqnp9xxhl9S6cPDOiiCnakoDZcIwkAKpbzkLtOPObHHXdcsYEGKQThasggSXM24vr4bJNmwIvH5HLmKFI0RvgWezEClVmFVIXC1dcbSk3QJ78mEkPGiEnTQ4wQkKZpDdiY6tJw0wUGIsKsic7gRn4cE2IxxRuyv6lcLtTIFBZg224tMXS4XlJRhSgdeeSRZS4lUqcXlNJ6Cp+o2ykt9Wc/+1lxKpWXVFWBKZEYDnqSNJGCkCOkqcjCdCLNIDjXoQzCagAiUWqh6uSIkqPCS4XU43d2NoM2tmu3xNDhGnphaWI2r7rqqlItXoSCHHYSp9hOef2bb755CYy3XiIxUowKaXqrI826nuZUB3IrhNk3yVhNdiQfU1OYBE1oDOL8/Oc/X4LaQ403yP3djTgTQ4fr5zrGdXNdSfLHH398ie1kDqGua2bJVLeTtH/D9Tf0T3+cSAwHPZGmDJbpTpoGaU10pEhz3wj2J+GIKfzMZz5TvLn1ejHYkzR7Q5HYu8yO6cWlGAqClKq62GKLFYclT/sSiy9R0jTPOuus5je/+U162BPDwqhJmtPZphkw+FTroQZK+3v5y1/eHHLIIYUwDWIOo3r9IMl2SwwdA103RCrUS2wnL/t+++1XyhdK+fW8sjEjU9lZAufN8BlawEDI+5OAnkizdgS99rWvnZakGUCYqjxtvfXWJXbQoFQuD2GGNNkelDEI2y0xCqguo5cVreg73/lOUdlVTaKuqwPLUWROdrn/t9xyS7lXAyHvTwJ6Is0IOWJwZ3ifzqRJFRTojzANSNN/mKM8VL/2gIvv3VpibCA8iemEo8jsmIsuumizwAILFLV9ueWWKyXpouhxwP2Il158T0xv9ESaUbldaIewGjai6QQDiAro5cF2JiOF6qcWJMmFlzYGXS3B+G2wlhg7sEEjRV70HXfcsWhISNOLznPMeSeulpmlf072vCWJCj2Rpnqaqo4LKH7729/eXHjBhX1LpweofWL/FJJg0+UpV/9R1aLi+OlzUpA2xW1CN5Jst8TYwn35+9/+XsxLvOyC4qnqwpNoTQsttFCzzjrrlAiIKD2XSAR6Vs8j91xG0A9+8IO+pdMDzp+jx7mLxVSujMPBNLQkUNfIACXdhJd9KC0xNnA/4l6Aaz1jxoyS/uvlT1uKjCJFVRQBIY1S2TmUEgno2RHEe84uZBZFhvapCuerBRRglg7Jdkk6YR8TxoIwVdcxIGP9mhCH0hJjgyDNOtQrQDNQDwBJUtG9BJGnegGrr756SUwQOM/L3ka8EBPTA6PiCIppV6dynGYMDOfNlvvVr361FN7gJX/GM57RbLHFFs2VV1zZ/O3Bv5X1gwBH0hJji27X231VQUkCgtqcKlKp1eneslMzu4i99aI03XId2+nvCLBv95uYehhV0qy951P1AWLjOuqoo0rMH8cBdU6WCSm7tn21z384LTG2GOyae67lp5tqwxQuyy67bJE6maAQqAyjXXfdtRQBYYKxLdu2Fi/WdktMLSRpDgOmVBAhsMYaa5SBJOOHA4zNq1bb2uc+3JYYW3S75loNL0B1AhT6IGGaVpi6zhRF6lx33XWbY445pjhDw0YamFvficmNJM0hggpmXneFb+Uw85QrPcb7GgUgXBNon/twW2Js0e2at1vAi/L8889vdthhh/KMe1Hysrv/asjus88+zamnnloqxpM8oVt/WmJqIElzCKB6XXfddSVSYJFFFinnK0VSCp6YP+fnenSza42kJcYW3a55uwX8TepUeo5kuf7665coCVlwJE/2Ts/CJz7xieaSiy8p3viQPAfqMzG5kaQ5AOKYDRjpdexYHAMRxydERTWdeoC4JvU5t1ti8sJ99oI0zYbpgwXFs2mHyi4TbL111yuB8VI22UW9bGvkMzA1kKTZQkiM8SkURViVfGWDw6dg9l/84hdlHWif60AtMfmBDKnip512WvPhD3+45K6rnIQ8qe4C5Y0JY8H4KPe989+z0rZ9JiYnkjRbcF4hIYjFNMOhArYGxQtf+MISi9meo3yoLTE14F56RnjQpc+aJC8cReydNBEV5A8++ODmx9f8uHngrw/k/Z9CSNLsAhKmKXflJ3P2UMNIEebXlpNcx+i1z3Owlpha8JyYe8jUzJtttlmxdSJPkRW0Euac7bbbrjiSqPZtdT0xOZGk2QWq4Xz9618vmSAIU14yr/nVV19dvKnOPdA+z8FaYnIj7qP7jzCjeSbYvcXqKjitJCDCFNvJcSgJQj0CFZbUVc1nYXJjWpOm42Jnqo9PZZsTTzyxBKx76J2bKWJJEykpTG/Uz7PnRqtfoLQTsZ0XX3xxkTCl1rJ3ch6q4E8a/drXvlayjiIRov0Mxnf9xr7qlpj3mNak6eFEhD7BnDFnn312CVinYskAWW211YqaHnOUJ6Yv2s90NGMhGnieEKdphRX9oLJT1z1TvovE+Na3vlXIsw19kF6DSNstMe+RpNkhTW99jb1SZW8Pufi7t771rUXqlPWRSLSf6W4tINBd2cCjjzm62XLLLZtXvvKVpU6BsYI8pWdS5dUx8EIOyRNqEh6o/8S8w7RXzwPCSOQa85A7H/PHKM7A0B+SaGJ6o/1MD9bg0UceLem17J3SMTfZZJPmOc95Tr+XXdFqc7KbG18REGMq0K1PLTHvMe0dQVQhE8SpgymzgxRg6o4jjjiizFSYSATaz/RArQ2/qcd50UUXNbvttluRMqnryFNKrthOMZ+qhNFqgjzb/WqJeY9RIU0PgAfhe9/7Xt/SyUOaJAFl3pC+h9h5mKNc2hwoIpwPawLaz/RAbSAYM7LI1OZU8CMmeNMUPV5zzTXLy9oEfbUNfSh9J8YPo0KavIOTRdKsj8mDGY4f9iZzY5MEygySs55UlRKJ0YBnjg1dgRfTCu+xxx6l1JxCx3LZo24nG6ixJI9djc8YP8ZcPLuJeYdRIU1vScRD/QjEzZ1IN5ltksHd8UiHow6ZlVDgunPYeOONS2EOKnsiMdrw3AXxidc0fnjZ5bIjTxKnECUquxhhBWEuvPDC/thgz24S57xHT6QpzVD4hNAcN/ncc8/tWzonaU4UOGaESMIURqRiTUyoJSBZLKaHOZEYC3j+SJqewXpcqGPAGSQ2mMaDPNnW5bV7kR922GHFUQT6COJMzBuMCmlSK0wuNhmmu0CK0tqQpAdTADvHDxKFDs2Xz0RitBGk6bMNSRUyihQ8VkEpJniTkcZBKTxJCJP1Mppj3qIn0jSxGvWcPQZpnnHGGX1LJy7YK+WQi8VEmCuttFIpJNwfi5mcmRhDDCQhGk+SKxSDERtsjiLPKH+BJq9deJIZXzkp77vvvn5TU2J80RNpIhrFV5EPR9BEkjQ9TPUD5W8ZGF/4whdKfByPv1CP//u//yvkH29/n7Ft3RKJ8cKf//zn5tJLLy2OouWWW6552tOfVrQ5NTvNfrr11ls3xx57bPPTn/70yami8xkdN4yYNKkIbDHiy9zQ17zmNROKND1Isx6b1R8yZGpdRROo4pw+K664YrEVebOHumM9XvPYpm6JxHiC3VPCxZe//OVmyy22bNZfb/3ykqfVUd2lY6rzyg5P6gx4lvN5HVuMmDTdVDP2CY9wI1+3/OsmDGl6aBCmpowbCRNhvvSlLy3H6u19yCGHlOD1tn2oJsq6JRLjDS/+v9zzl+bqH13d/PCcHxYtSRyxZBL2zgUXXLDYQE8++eQiwCDPEvmRj+uYoif1nG1FUV5ERNKs4zTnJZBceCjVMVQoVkiHcI7nPe95JcSDUb0bGQZJtlsiMe7oPHY0n8cefaw4kATGmzWAV13Eh+eZaYy5icpuptQZM2fMzmPPR3bM0BNpktSoCEhzotk0SZCOj5NHIWHGdISpPJeMiygkHPagIMaaKOuWSIwnuj2DIj9oTWq9CkWSjIE8NVKn5/xDH/pQmcdIbGdibNCTTbMmzXklaRbbZedYNH8HZFJ8+9vfLgVgxb4plECVkQEUsZixbU2cA7VEYjxRP3ueUZpTPN/ijAW9C/dj53z2s59d1HVNosaGG25YUoNvvPHGUnCmHhd1WnD0XS9PzB09SZoyGpAmKc7NEw4x3nAc1BHNA+BB8Ja97LLLSmiRY0OYKsxQX4IwrWdbn+2WSEwUtJ9Nz6xGXecokqu++eabFzt9BMaTPJWi23HHHYtUetNNN5UCyRDPPPiMLKPE0DHpSbN+oEB6pNS0LbbYooRoyFYy8ZVjq7N94u1dP0B1P4nERED9XNaEB55heexKzwmdk5VH0uQoYuuUjolMt99+++aCCy8operaz3f7e2LumPSkCfWNZ/Ph0Wfj8eYVvH7SSScVNQUQpbc0m2YdHOwzWiIxUVA/l/Gi1/wd8LeYabGd5l0neZqjKKTOF7zgBcWWL83Zs5/oDaNGmuIf5yVpenDYWE25y0DugaGiKMOlOjZ42AQDe3A029QPZbREYqKgfi49r55bz7Hx57tWQ9iRwjkf//jHS/rl/PPPX8aCaYXD1mla4btn3p3P+gjRE2kio1122aU4guTLjgtpDnCfHYtAYMfheOSVC7z3e4RghJQZas5ALZGYKKifyyBNzy/4rG2S8Z0WJaTuwAMPLMIMlR15kjrNTPCe97ynpGqaBE7qZj7zw0NPpKlgxyc/+clCUMhqrL3nPH91nUvHoLFVxgySqhbJ+JG7e+aZZ87xJo6HL5GYjPDset7jOY7nv/5NA+RK8xL4bjZVkibi1DhGhSdJgSaVUu2tH9smBseISRMZCbbdaaedClGxaY5VnGb9gCBO+/Y3IEwFXVUtUhHGWxVhKh7CjlkepIz0TUwRBDHOrcW6xsBVV13VfPGLXywO0fCw08YUAVFBnkmLZJoYGkZMmlRdBQME05I0x5I0cV6RMjtEiTBDehSLKbSId5Cxm6d8w3dtWKbduO/e2fm48RZOJKYCamIcrPULGZ2/gTR52mmnNdtss03JKIpUzPBH0Bg5ikinxZyVGBA9kaY4MYSFNF34sc4IQpaPzZpdVd2Nveaaa4rdUgED9hqB7N8//fv/lA0RD04iMdlRE+NgLUgzBAx/s19KfVYRXjIKIUMqJvKksq+xxhrNwQcf3PzkJz/pj+tM/DN6dgSxixD5x4M02TPtF2Fef/31pZYnT7mYtKWXXroUapVrHg9NPDCJxFRBmxwHaoH6O22N7ZLUyXy17bbblnHDrEXyRKLG0zrrrFPSj8U8G0d1f4keSRNBEetdbE4YFdHHCgjQzSNFstEga1WLELYCyPvvv3/JfHBc4DP+TiQSc4Jpi6YmrlOxD+F5IXXyUayyyiqlMhiVXvnEx5+YPZaMQWMxxmPA3+02VdEzaQo5cpFNUFZPrDbaCAI0V8p2223XvOhFLyp1PGU8CK0Q1D6Vb1QiMdowpkiTtDaVwHjUOVIRJwJVOf4tb3lLs99++xVBJcKTbBek6dP3IMq6TVX0RJrE/IjTHOvpLtwcnkBqg/RIoRNUC/tHpLzocfMSicTQYWyZveCEE05o1ltvvRKeZGaDcBSJ7ZSWrOAxR1FUCAOmMv6NNmFO5XE4YtJ0oX/1q1+VkCMXtj3v+WhDpsPXvva1ojbYH+L81Kc+1R+g60a6eYlEYvhAcqonqYxkmo1lllmmP5uIz0BZRc6jvffeu+S6B9pEWbepihGTJoJy8YQwsGkS43/4wx/2LR1dxEx9G2ywQQlcZ8f84Ac/2Fx77bVluRvkeEiaiURieGgTnFBCGt0OO+zQvOpVryrmN+SpSc0UsWI8mqQwBJWaLKNNVfREmhwvjMjPfe5zm4022qi5/PLL+5b2hvqCq+LiBslqsB/hRWuuuWapi8kTmEgkekM3kjNVjOSVL3zxC81b3/rWImkGcaqetOqqqxZNj/P37rvvLtt0eunvq93fVEJP6jmvmukukNlWW23VL/n1Ahdb30DtPuecc8pNI2F646222mrNGT84o8ydkkgkxg6I08yYzG6SWHjYjXU+DCFKiFQ5OkVA2DpFtoS2N5WJsydHkDhNVY68eQS5m2htNBAX24RS1H+VqQWvI09l3u79y71zVKBOJBJjB2Ro4jbaHZWdA5Z3XSPMyAbEA+ede16xi9aYiuQ5KqRJAnznO99ZUhpHA95wd915V7PXnns1iy66aHH8uFGyFagCcSPShplIjC1C6wOe8uuuu6750pe+VLzshCXqOoFmkUUWKRwgx90cXEKZbDsVBZueSDPqaRLXzcOsqlCv0K/qSSpRyzJyUxQWsB/xZAHrTcUbkkhMFBhfZsKsK4sByZPZ7P3vf3+ZCVO8tHFKZfddppEykfhhKuax90yaip26aET0kYYc1eQntOhb3/pW84Y3vKFImNK6dt5550KYbkC5kekpTyTGHp1hiTCZwmoYg0L82DHNxa7mA/sm0iR1im7hKDruuONKDDWSrSXWgH7qsT9Z0BNpCm6XRil3VT1NXu7hXgT9BAna9oorrmje8Y53lAu/+OKLl7fWFZdf0fzj790nREskEmODoYwxxMmDLn5TeBKtk9TJ1imu0wywRx55ZCk9F9Eu+kSihKDJKPz0RJrSKHfbbbdygThpiOzDIbK4eJpc2KuuvKqkSHL8sJdss/U2zZVXXlm86LF+uyUSibHBUMcXLpBkcszRx5QQRAKUgHjk6dN32iJHUszVBZPV5tmzpKlwBtKUe24u5uEgRHafyNEFl+8q/3X99dcvFzlUg5oo65ZIJCYAOkORcEMdP/zww8v4VbeTFoo8hSpJTqGykzqZ4Sbr+O2JNOWrKs/GpimNUvHfkWDGjBkly0AhYW8m9kyqvgvrZkCbLKMlEomJA7zAhilb0JxdioCot8s/YWwrtPOBD3ygOIo4fCejo2jEpEk6jIpDLoZqQ9/97nf7lg4dURRVSBF7yMorr1wKB8ycObPsI5w/A7VEIjExUDuMjF2O4lNOOaVokMsuu2yROEPqRKYEJfbQdmznRMeISZPzhpgtU4AILuRoOFWObI90DzjggEK43kRLLbVUs++++5Y3EHhrhQrfjTC1RCIx72EsGq+hGQbUjbj66qtL/Kb0Z2Oc5Bml50wrrBDPr3/96/6xXqP0O6vDA49PHPtnT5ImKVGGAPVc9SE2yIHQJjkpmIqcsnsIjucp15e6fZxCUG8Tf7dbIpGYmDA+EakmKQU/0Cr5P4QoxeyYBC7Ck3q8pNO6pgTCfPSRR/s1zomAnkjT20HuOfX8zW9+84BVjpxsHVakCId8VSK62C7iOlFduJG6mNaJFtsP1BKJxMSE8RnSo7HP1sl/ccqppxSp07xE1HVmOTU8V1pppTJljawjPGDbImU+9uRkihMBPanncs0VJ6Val+D207sHt7t4RXTvwIVjBPa2IaaH591MeBFaBEGIQY4DtUQiMTFhfOKJNuHN+NOMkj0oxpu6HrZOhY85injeDznkkBIDGrwB3QLt5wVGTJpE6AsuuKDkm1LPV1xxxbmmUYrRkjVkXnKxmLaTTSAMIcpLxQVuk+NALZFITDwYm0GYNfEV0uv8l6zCw44cN99888IfhC/kSfsUKG8KDvUsOIUDE2HM90yaYq/EVaqnyR45EEiRSPXd7353EcddIBdKjjkydTFcXBcaghTn1hKJxMSDsYwjasJsw/i1XLw3Z5BQQ9on4pSOSercdNNNm69//eulylKtic5L9GTT5D1XQZ1RV8S/+ZLlpLpYmpN86KGHikquQLH4rAUXXLBImFKspFd5iwT5JREmElMDQYhDGc+4RMy3mhOEMF51QhXhikZq1lnpmKJzEGxbsBpv9ESaQobkhpM0OYLMLXLiiScWm6V28sknlwvxzW9+s9lxxx2bl7zkJcVbptybGe7MMZRIJKY3cAkhi4OYM/jzn/98sWsqN0fiJHkGxwhJVOw8yNK2SHQ8CbQn9fySSy5pNt5442KDEDbEqCs4nWdsrbXWKiepsrM50ZV3Cy+ZYFdSqRNOJBLTG7VZDtS0UMdCERAO5pgZUyN4ibQRvkToos0GYQ5mChhNjJg0qd3SJhGkkxGsKsgdeQpBooIjU5JlvC00JaMuvfTSCWOfSCQSEwCExE7jIQ+13lQbCo/zfRC2CF34RKiSAkFR8JhPJEKUxgNzkGaw9VDEXLZLNoa3v/3t/YQpUP1Nb3pTOUl/m6UyyNI6PondLsZ4vhkSicTEBR4o4UQdTkB8wQsC2sV1cjBT2WUOEsaiZqeEmHXXXbcUCDGDpmrxg3GK/ofCbXNDIU0EaDpO6jaxl13BVBYRaN4NthFbqew9o62KzbvvvnsRq7/xjW80m222WbFJtElT2lRk/KR6nkgkajJr/w2IUOk5oYmidBQmD5WdYKb0HJX9rLPOKiSLbLU2gfoefQ4GvMT8WJsMAkKm5pMbqqSbupg8VEhwk002KdNzHn300YXlJdSHsTXgoIjGYqyIzWwPDtrOpEMJLZLpY8pd3i9vBidpKl5vBBjsrZBIJBIBZMUkiKs4nCXE8JMEeUqSwS3iPq0jML4tlNWE3IZ1qfl8LaeffnqZwPG0004rQiBz4rU/vrakeD780MPNfLzcpMJlllmm5IBKbRRYarpOE8O/733vKxti8Jo4EZ4wAXP3EJmjnJtgVHOHBGFSxxFwRP77/sADD5Q+EolEYjgglAk7Uh0JeUq9ZOPkR2EiZPsk+B177LH9sZ2DkWVAv7feemsxA/C7qLqGCxGxWNEtt9iyTCh30003NfNtueWWRRJEnEKExFMKWseysn2wOckTGVLXwQEgTQe/yy67FJZn28TySDQmluckUi4O85NEgzSjAGmq54lEYrjAPQQvRX+Q5z777FOENsSJYzijlaJTthL3IM65cQ0+ogELssdV1H7kaQrx97znPc0rXvGKwpM77bRTM98SSyzRr1qXor99sCOR+KoXkUIxMDsnBOHFxGoOVqfCi3yK6rfNEUccUdIjb7/99qKu86Yj4qif181mkEgkEgMhBLbgIP4R/hjqtDoYnEOIk9rubynbiiFzFA3EN9En8OuQLkmvu+66a3PxxRcXAVLfiqQLqZyPlEgFr+fuCES9TCuTNm+++ebyexww9Zyk6QAjgj8Ms8q+CX4H6+nHvpxE2DSnKlyfwONP9Bmf/e981svaiBs3XMyt30SiF0ykZyuedWMlHD6+04I5sE2/I9uQD0V4EkGN1BlOarGdbKM19IXPfLJpbrXVViVzkeMJCH7Cmzi7mS3nIxHKzpHqCLExsGPamVQmoUQ/+tGPyu8OEmsrDYeNESbvOPJkB2XDvPHGG4sIbT3ky2vuJMw0GfZRHngnMJFanQYax+ezbvVyzQ3THvrHQ+X3uIbOsZS28r0vpAJ5+m5ZtFjfZ2wf8LvfPBzdEA8RxLpxPPoeKvRh2+grkZjIaD+nvhsjCpjTkNdYY40SvcPOiZ9M1LjCCis0e+21V3FuC3sMnotPuOaaa4pPhomRuRFh+o2kyU/D7zMfFj7wwAP7nTN2HgeEMA477LCS9mhl9k6w3AAjQSLNCGBHrnJHHTSPk4rNUp6EIGF/YjPyZYdwICZTmyjNW8r5OWaiPIOvY3SBRQlolrWbbdl7fZqb/a4772oe+OsDJatBkea//+3vzf333V9MEm6q68bMQaVgqNa8fJhGqBqM0cIrfCeRs9vYNylfH0GwCNGLTuoZU4p+PQjK9Tkeb0weRMus75757NYclxoA9sPkou9u62WbPs0z4JmK5y14wfdeWns/Wrf1BmqOK8ZRvf1jjz6ZSok4xZCrh7H88sv3FwGhCTMfIsWjjjqq8FeMi4AxjSClbfLTINntt9++SKt40LL5SIZKMIWkGdCZAa8KEc+3gHWDMZY5+CBNhKlRv02wxiZAsqSKs2VifYTqwBdeeOFCrJaxb06k5rgcrzRPFzaO0W/iw7o169hOY8JgfJb+9dGdP9p8cOsPlotO8t5zzz3Ly0lTuJkDTrETRUzEmFnOoO13xmffmTisYx9Cu0j97pUJ+vfff//yXU1CmoLK11QTnj7ONsZrD41K2QcddFDZxrbWq5vf9OU+Ok+OvDjObNO3eTYUBI7nQ/ihSBseZMv5OEbSPIfdWrd1B2qOSfO3beN449gdr/FjLIgEoqpHnDipkxTJV+NcfvPr33QIrdBaAUHJmLMN4uTzIbHiLeOWMDifHwyuOUiz0wn2xdgGsg3lkpNEAkiTfcAgczCDtTjgydK8kerUz+E0N8XLw6fv3nK8eW4CFYGBmZ3FMhK6z7AFWy9+10e8aKJxuPmNmuCG2s5vQrv0HW9UzTX33bqqxtivbepmO/1p1Bjb2cZDpb+p0Jx3tG7LR6ONRv+2d6+69TNY37Esto/me71dfG+3WN5u8Vz427Miw080jHJtfo/tPSuxv/a+47t1tPgtvndr3bZvN8dkeXubWBbHZ5ljj/FWN897RAXVwHGEJts5V3ZMIZVsnLRu6vp8Bo5CwFS5Gh1Bt7AutkaaJBHqZoAtj+ooKF4fBrkWg9EnojCo7dRg9N068bsDRxbWje0st270ZbnvPi2PVi9DNpr+9Kt/vyMVLfqr9xvbRd/RR71f6/u0fhBUrB/9+R79Oy6/RYs+Yh39uqHW9d110admXTe9Pj/bWhbnodnG8TjW6E/zd/Tp07ZxPTR/x3frRLNfD1oce1yTep2RNi+OOObxaLG/OEff48XE3t5ev9cW98Y+NIPTPrutO1CLY43j9LKLa+ZTf469Pq9ose/6PKOFj6FejyDg92ixvL5edd/OR/Pds+EZqZ/b6DfW8V2LPuK47Mtn/G4dyzR/Ow7H7Pj8pm8t1rHc9tG/36JfzXfPbd2PFtfCuvoz7uzfb8YMVZtJjuYcYE4kaSJJTm7SNtOisSk66NRTT23mo0rT17nlkSB7ASmT/YzoywZAlOV6Z+MMsCOwwSFW8/0cf/zxJQcUG4t1ElxKfBbXJAYUe1NT9Um0VlKOlEp1jO1N3eu73xlh2UYl7Pvuk21UE15gGZHcvOuhAvPQ83xRV3f8yI5F3fQ2cfLMDMR26q9977b7bmUbpO+YqNRE+kMPPbTsi2qsOQf96su2VGLLQ00hpevfb85d32wgoRY7dtEJ+rB/thTb2i8TgHXdPC8l1y2ac6O6U8up2vavUdWt7zjcM+u6Vq6DdWV12ZdSfL5bXyUq27gHPpkVwkRiXeceao/J7fThuo20OV77WG211YpphonDc2Z/zDaj3VwX/SviQCPyvNm/74KUSdrC6uQpdzvekTbXiWOTFEYNFAz9lre8pRyTa9Btm3aznutiey8vmp9zcE6O1zVkl3Md7c95uZ4+7dt2qonF9vECpU5yfLjPtuX1ZZN74QtfWAjBfvRr355PfbpeTDuel7h2rpvxT8r0u2OOT307dwHmztlxq2gW99t2+EPAOYnNb457nXXWKcfMv2Eb0TYI2TH73TWxD8KcPiznsPZd4Lpjs1/3Vd9iNB23CkjOPYQOBE8o8LsMIn1aVyiS77zjTIwBWUdIk3nM9REyyb9hvLpWrq/xOt+3v/3tcjOcCJuYQYiYDHAXygXBthwO3UBNR54kT2FLnBE8txwQgt85VIjAyFW8pt84G3y3jAPC9rbRB886pwcx2HfLffd7eLjt0zL9OCkSMOeJE2bI5VjhEDn/vPNLoL6y+o6fNM3hY73bbr2tuf0XtxeHjGO64447yvHZn315gTA/MFFYX5Asp5B1nCNHjWX6Fh1gO8dMvOeEcTP04xy9zfThN04iqav2y3lkEinXxzm6DnGOzs3+LPPCuuD8C4oDTYvj8GJzHezXcdgPm4tjcP6+O39prfbld5/OxSR4ljku5+5c7NN2YtVsM9LmGC668KLmO6d9p6SkxXHb32g356LpXyKF6VRcM8t8/8pXvlJebl7IQk5cy9FqzlOtBi9C44YUIqbP8VjWbZtuzbESGrwovQA5MfTheFUSc+zOq1zXzvV17yy3b9sZwwjA9lq8sI1j9SH0wSapb42QQDjQr30bE9bTjz7tQ3afl7J1nJf9ey7i2XDc5513Xjl3c5vr5wff/0HZl77cD3V0jznmmBKuo6/zzj2vbGcfrpNau87VPvDNQV88qByDfTg/x2DfzlE/7uc5Z59TPu3XeRBW1PAVZ04wwlXOXyP0EKCQHnusY7Qu4cZxGuMcSgERLo4bAXuxuEbGKh7QD4ImYM5nwOmQGu4HzVuJOOpNQAJBTCTQgUC8jRYercEaKVV/IdVqgegjROb4Hl6z2KbeX/13NDPYmfoTqcQ2sV+fpQRVXxhQvazuv/6MFvuqj63017fc3/Hdcscd38un/Vbb+KxfBn6r+451eAdL6+tPi2NpH0csr7evf9dH7KteXrdYZySt7Mf171xL32MfY9Viv3H/NINBc/9d2ziWbtv30tr7jWPptu5gLfqJbeM+1OuU753r6rxivbK/znNRn6/P/r761o9xEOvVxxv3KtYpffa1/nUGOKZYppWpdjtNf7Esrr9Pedt+iz5iW5+2e+Th2edVvnf2G8c6x3F1zjWm9I3ziP3X+/J73ep+43s9fsDxHX/c8UU6Zo5AugQtfRJqwlRZqhwJbSGVkDiJvGwDGlWT5EZqnBtix+CiODAXr/ZMgfWcIMR62twQFzdO0rYDYSQz1umz3JDOsQzWN9TnOhqwP61cm841G2z/lsVDAgMdS7ffB/ptbuc7IozuJRoU7evhOYm/u53zWMD+Y19jcj0D7dPxvfotrkM/Bjj9uO/WL8c7wHqjAfsyrpDccK5N+5pGG+xYLe92z4M029xgH/G80B5pJswByJHUSqOzHEeStpnM+utpUhuJzpEEz2iKcans1Don3IYDiLdUfaD+jpuhxd9+dwCYOy6IzyAqzd91f/Gb/VsXop/og/QW32N5jfZ3sG5sH3/rx34cn/5K333H3W7WL/vsnH/8Bj71Y7njto4+4ns39G/f+V/e0i3iLH0+Mft77BfBh6QM9bWzTvxef8a5QKxfrwuxXr3ucBF9xLmPJerjLdfFPemcU/916mue1ZGez2DQZ9znWY/PfoaGuy/r1i3Op91HWdb3bMU+2s2ykMD6+6nGqeOM361LKovfSr+tvupnLFDvo6zTt61+Bnqm/Bbr1McXy9stjrHuu/xtfPT17zPOKfqJbWrEulosj/OKY/a342LqY35gemDyYorzu/X8ffNNN1dFiDvnSDyW+sgWwrHAKMu4zUGis+g8Di5OJg66G+KAfYK/HUScWL3cb3ERYn2fcWKW+x7blD46q8WxRJ9tRF81YpvoK9bxt+vgE7ptC/377Fz8Njykfo9rE+sOdp0C1u32oMZ3n9G/z4Df49oN5TrE+u11S/99rRfYvlyfAY5lLFDvr1zHvhb3cixQn2e5btU9GSni+mtt+C32NRDiuYt1fDpG99tn/Xv9W32dfB9oP9GXfcS21vU9nim/RatRb2u9GvW68Xf0Eev6rPuPYxgKok+I+6SvwbaPc6q3naNyO+jEipw6jLBUdAQq2yWyS7T6Yo8H4iK1WyKRGDp6HUPdth9u6wWj1c9wUe/3n0izBo8zCZP3iL6PTMGG8UYZL9QHXbdEIjF09DqGum3faxsORrpdr6j3Oyhp1mgfZHQwXoj9tVsikRg6eh1D3bbvtQ0HI92uV9T7nStpWokaHm08pcsa9UHXLZFIDB29jqFu2/fahoORbtcr6v3OQZr1Ai0Qds6wY84LtI8tWiKRGDp6HUPdtu+1DQcj3a5X1Pv8J0lzoAMa6PdEIpGYThiyTTORSCQSSZqJRCIxLCRpJhKJxDCQpJlIJBLDQJJmIpFIDANJmolEIjEMJGkmEonEMJCkmUgkEsNAkmYikUgMA0maiUQiMQwkaSYSicQwkKSZSCQSw0CSZiKRSAwDSZqJRCIxDCRpJhKJxDCQpJlIJBLDQJJmIpFIDANJmolEIjFkNM3/BzW7JP+FAxNuAAAAAElFTkSuQmCC)
![straight capital delta Q M R tilde straight triangle P M Q](data:image/png;base64,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)
By similarity we get ![fraction numerator Q M over denominator P M end fraction equals fraction numerator R M over denominator M Q end fraction not stretchy rightwards double arrow Q M squared equals P M cross times M R](data:image/png;base64,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)
Hence proved.
Related Questions to study
Maths-
In the figure,
then find the value of x and y.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANAAAACuCAYAAABHjIPFAAAgAElEQVR4nO2dZ2BU1fa3n2mZlEnvIY30RkJIQLqC0pQioFRR/HuVK00FQbDX61WQdm2IwBVBFCmKXqkK0kRagIT0TnpvM5mZzMx5PyC8FoRUQpLzfILMzJl1zpzf2WutvfbaEkEQBERERJqFtL0NEBHpyIgCEhFpAaKARERagCggEZEWIApIRKQFiAISEWkBooBERFqAKCARkRYgb28DRDo4DTUU5OdSXNkAgETpgLuXOy7WZkja2bRbgSggkWZipOpyBse//4Y9CXEUVILSVE9ltRWBQyfzfzPvoYezZae/wTr7+Ym0BYZ6ipJPsHXLN5zOdWDo9KUs7u+DraSazB8+Y+WmrXzt5YrzA3fg2cnvMDEGEmkiJjSXT/H9xxvYnW3NmBfn8MiIHnjb2WJr603k0Hvp6VxL2sXz5FY0tLexbc5Nnw8NFYkcPn6GpKxqpFIJCAKC1Bxzt1iGj+iBl0ouqrArIZRz6dS3/C+lishHljAq1AXF719XmmMml1BVXkadWgt/fLXTcfMB1lBDYfIBVq0+ilP4XfSLdEWiLeP85l/IMi7k6TEhuFjIboGpIu2PCV3uWY4diqfUcxCz7gnF7k/vqM5LJq20GssQV+wtzNrFylvJTQWkcIlm3H1D2XrEkr6PPs28sSGYlVxg61P/x6ff/8J9/X1x8rQSR6EugZ7CjFROn5PgNmYw0U5/vn1qKEg8RXq5FaGhPfByULaLlbeSm9/3BiM1efno3UIICeyGg1yCmRk42BuRyCVIBEmXSFeKXEGjMaGXWuDhY4f9n++emgR++fUUtT4x9L4jBMfOPwDdXEAGXQnnj6Vi7WSHp70SXW0xiQe+YOdFJTF9euJrZy4KqAthaSnBzs6EwWjE9Lsf3lSRwYHPvmZzgj19Ro9hSIBtJ49+rnBTF05XdoGjKemk5lfycc0FbEx61DUC3act4MHRoThZic5b18EMey9/vDy2c+T0Xo4PDWWQmxyhNpm92z9j+f/K6X7Xkzx+TzQund97A0BywyXdgpGs715m6c48PIIGEu2pwCgxx9ojikF3huLSyXP8In/FqKsi4cinfLzpa86Ue9JdJcWkluMcHErEyDGMjO2Jv0PX8UluLAFjEedP5qLyGMjMeY8TaX2LrBK5bZEp7YgaPJOHDfa4/pKJSzcvzMy8iO7Xj5gQB6CBBgNIZQpkXUBHNxSQPv9XTubrsQjrhqM42ogIRvTacrLPHyXux2MkJBfiLLFn7LTeeNkbKCoooCb5AOlKb0J6DsHPqr0NbnuuLwujluqabE7t/IZz5Vb08/BEJTUhIBUTBl0ZQwlJx3ay82gdgb2GM5ADfP/1FlYlJ+BmARJBoFtUTwbfNwSHLpCBg7+JgYxlp9mwcR2bNv9Ins6B7v1msGjJQ9wd7EAXuS4i10Oopzw/m7xqS3wCfTCvLSQ9MY1yoxGjSUAikWDnE0yArwfWXSS3dF0BmbTlZGRkkV9ej1wqQaJ0xifIFw9bJVLAaDRiMpnawVyR9kIQBBoaDEjlciyU4mP0KjfOwv0JQRAoKiri4sWL1NTUNP5LJP/f8RP7OLYuV69tW19Xg8FAUVERgiDQv39/YmNjkcvFwLhJV8BoNLJz5042btxISUkJ5ubmfxDH9ZBIJBiNRhoaGpDL5chkYt1cayEIAgaDAZPJhJmZ2U1/i+YglUoRBAGtVotWq8VoNDJlyhTCw8OxthbTsk0SkCAIlJWVkZ2djclkIiQkBAsLixs+/XQ6HQkJCZSVlREREYGnp6c4CrUCEokEnU7HyZMn0Wg09O3bF3t7+1a/tnV1daSlpZGXlweAhYUF5ubmSKVdJMi5CU0SkEQiwdraGkdHR+68804WLlyIra3tDT+TlJTE22+/TWlpKUuXLuXOO+/EaDS2yGiRKyNDZWUlM2fOpKCggJdffpnIyMhWjU0rKirYtm0bqampODk5YWZmhp2dHf369UOp7CKlBjehyU6sVCpFJpNha2uLu7s7NjY2N3x/SUkJCoUCc3NznJ2dcXZ2braxIn9EqVQil8upqKjA1tYWFxeXVjt2VVUVhw4dYtOmTdjb29O3b18OHjyIvb09QUFBoiv+G80ehwVBaNTT7qpL0dj3izQeQRBQqVQIgkB1dXWruW+lpaVs3ryZlStXYmZmxqOPPsqwYcOor6/H3t4eNze3Nom3OiKiI9uBkclkuLq6olAoKC4uRqfTtfiY+fn5bN26ldWrV6NQKJg9ezZjxoyhqKgIhUJBcHAw5ubmrWB950DMQ3ZgpFIpLi4uyOVy8vPzqa+vb9HNnZeXx7p16/jss8+wtLTkmWeeYcqUKZSVlXHy5ElUKhUxMTGYmYnzQFcRR6AOjEKhoF+/flhbW3P48GFKS0ubfazi4mI+/fRT1q5di5WVFQsWLGDy5MlYW1ujVqtJSUnB2tqayMhIcf7nd4gC6sAoFApiYmKwtrYmISGB/Pz8Zh0nMzOT999/n3Xr1uHl5cXChQuZNGnStQRRSUkJZWVluLi44OnpKaawf4d4JTowEokEV1dXQkNDMZlMJCQkoNVqm3SM9PR0Pv74Yz7++GNcXV1ZsGABDzzwwDXxaDQaLl26hEKhICwsTBx9/kSLBCRmYtofhULBqFGjsLKy4syZM1RXVzf6szk5Oaxdu5bPPvsMd3d3Fi1axJgxY/4wNVFXV0d6ejpyuZyAgAAUiq6wULvxNFtAEomkUQKSSqWi0FqBv2Sof/u/VCqlX79+WFhYcPr0aeLi4jAYDDc93uXLl/nggw/473//i5ubGy+88ALjx49HpVL94X21tbXiCHQDmlzKo9Vqqaur49ChQ6hUqmvzEFdf/31xo0QioaysjNzcXBoaGqirq2v9M+jkqIvOsm/fHn5NtKLviJHcc5cLl7bu4kSSlNgpIxkY4YFXt24MGjSInTt3sn37dmJjY3FycvrbYyYnJ/Phhx+ydetWwsPDmT9/PiNHjrxuBk+tVpOTk4ONjQ1+fn5i/PMnmvw40el01NfXc+7cOXJycpDL5TecwJNIJKjVagICAsSnVzOQKqxxdnNE/tOPnDiipTQ1FKsKHY5+fthamSEAFlZWTJ48mSNHjnDkyBGSkpLo37//dasFEhMTWbNmDV988QXR0dEsXbqUu+6667qlOXq9nkuXLiGVSgkNDRXdt+vQ5Dva0tISlUqFv78/gwYNwtLSEqPRiEQiQSqVYjAYkEql1/59VWBubm4EBAS0xTl0aiwcgxg0whd3STX/2ZpAsjGEx2ZOIcTfkd/LIzQ0lGHDhvHZZ5+xY8cOgoOD/1DaIwgCiYmJvP/+++zYsYNevXpdq038u7q2uro6zp49e01AFhYWbXy2HY8mF5OamZlhYWFB7969mTdvHvb29hgMhmsCMhqN1+Ieo9GITCZDEAQEQRB/gGZjhqtPNE4WtZiFd8fzT+IBsLe3Z8KECXz//fd8//339O3bl7Fjx2JpaYkgCJw+fZqVK1dy4MABIiMjefHFFxk0aNANR5X6+nrS0tKQyWQEBweLBaTXockj0FV3TalUYmtrK64JuRUIemo1RhzNq6irK6NKDSpzE0ikyH4LSaRSKeHh4TzxxBMsX76cDRs24OnpyR133EFcXBxvvfUWBw4coG/fvrzwwgs3FQ9ATU0NmZmZKJVKQkJCRBfuOrQoKBHX9bQtJoOWutoaCjOPcbG0Fktvcyq1l4g/p6LU2Ytunt1w/13SzNbWlilTppCWlsbOnTtZtWoV48aNY9u2bfz0008MGjSIJUuWMHDgwJuKQafTERcXR1VVFdHR0djb27fx2XZMxKj+NkZTmsTu7Z9ztNyWwfeN5+6hlqzfupuPz+uZ8n+T8LtOSOnq6srjjz9OcXExP//8M3FxcZSVlTF69GiWLFlCeHh4o0YSvV5Peno6ZmZmREVF/SW9LXIFUUC3MUobT3rfOREfwYlAf3/clN2YNt2HwdXWBIS6YnudX+9qvNK7d28OHjxIZmYm48eP55VXXiEsLKzR363X60lMTEQulxMZGYmlpWUrnlnnQRTQbYzCypngSGeCr/3FkaAIR4Ju8rnExESOHj2KVCpl3LhxvPnmm00SD1zJwGVkZKBUKgkKChLjn79BFFAnQhAEzpw5wyuvvML58+eZMWMGCxYsoHv37k06jsFgIDc3F41Gg6+v702X7XdlxGnlToJarebAgQPMmzeP/fv34+TkxIQJE5osHgCtVkt8fDwGg4GgoCDRfbsBooA6ASaTid27d/Piiy9y4cIF7O3tKSsrY+/evSQnJzf5eFqtlnPnzqHVagkICBBXoN4AUUAdnIaGBo4cOcI777xDamoqkyZNYvHixbi7u/PRRx/x6quvcvHixUYVmF5Fo9FQUlKCRCIhICBAnAC/AWIM1IHRaDTs2bOHRYsWUVpaykMPPcQrr7yCk5MTYWFhvPvuu+zZs4fq6mqeeOIJhgwZgp3dn7cF/iMmk4n09HTS0tKwsLDA29tbTCDcAFFAHZS6ujq+/fZbXn/9dUpKSnj00Ud5+umncXNzA2DEiBF4enry0UcfsW/fPpYuXcr48eMZO3YsPXv2/NtRRa/Xk5GRgVarpWfPnlhZdYE9SlqAKKAOSF1dHbt27WLFihXXmis+/fTT+Pv7X3uPXC4nKiqKF154AX9/f77++ms++ugjjh49yowZM4iJiSEoKOgvff0aGhrIyMjAYDDQu3dvMQN3E0QBdTDq6+vZuXMnb775JnV1dcybN4/Zs2fj6Oh43fd7eXkxd+5cevXqxeeff84PP/zAU089Re/evRk2bBh33HEHYWFheHp6IpFIMJlMZGVlodfriYyMFCsQboIooA5ETU0Nu3fv5rXXXkOj0TBr1izmzZt307jGwsKCu+++m7CwMGJiYti/fz8JCQm88soreHt7M3z4cKKjo/H09MRkMpGRkYGlpSWenp5iB9KbIAqog1BUVMSuXbtYs2YNAE8//TQPPfTQTcXze9zd3Zk9ezbjx4/nxIkTJCYmEh8fz88//8yWLVuwsbHBycmJwsJCcflCIxEF1AEoLi5m8+bNfPLJJwiCwNy5c5k+fXqzemHLZDI8PT15cNIkEARSUlI4c/o0WdnZ5OTkcOzYMfR6PZ6enuL8TyMQBXSbU1xczOeff86HH36ITCZj7ty5PPTQDBwdHa4sVDQaEX5bAfyX1i2CCZPJhEkiRfan1yUImASBkJAQQkJCgCuNRmbPnk1lZSUjRozA1dX1Vp1mh0UU0G1MUVERW7ZsYe3atUilUmbNmsX06dNxdHRArynkzLd7OZaYicZcScSoqdwV4Y/Tb1139SWpxB3ezY/J1WhVfkQNGM69vTywUEgQalI5cOBHjl4owsy3HyOGDqKPrxVGo5Hq6mocHR3p1auXWMLTCMRKhNuUvLw8NmzYwIcffoi5uTkLFixgxowZV7rtmEpJO3CC/BINdh6u6PP2s3Hte2w7k02dAEJVLse2f8rnP2ahtXXBTp/Dkf99wde/FtFgrCbxTBoXU7So3N2Q18RxNvMiORpIvJRATU0Nfn5+YvatkYgj0G3I5cuXWb9+PRs2bMDe3p65c+cyceJEHBwcADCV51AucyTkviGEB9hTdknFu6+t58BP8Yzs4Y17+UXOnjmPJvIpFv3zPrzLD7P8k138eC6Xe0Ll5BqMeN/zCBP6OKApOsyPiVoqSjTk5OSg0Wjw9/e/6b5PIlcQR6DbjJycHDZs2MDGjRuxtrb+i3gAJBZehAyMpbuPA1IkOPsO4o4Ae0xqDVpdAyb0aOtM1BTXUFlvRIsMhZMtnt6WWChtUOihvriAgooKiopKUQsmJGZy4uPjqaqqws/PTxRQIxFHoNsEQRDIzc3l448/5quvvsLa2po5c+YwYcKEP4gHQKJy5XcNqzDoajFgQWiYGzYqM8wVEcREh3H0yCE+3eXJgx4alGY9GdXXBzuVBT28crm467+89IMamb0Pg++Lwt1WQl7eleb0fn5+YgFpIxEFdJuQl5fHmjVr2Lx5M76+vixcuJARI0Y0opRGgjork/SG/sSE++NoLkFmHsjdUx4kT/0f3nv/HSp6DOeReROJcbNBAriG92Scwoqw3CrkToGE+HuTlxRHWXk5UVFReHt734pT7hSIAroNyMzMvNanOjg4mGeffZZRo0Y1ahQwqkvIjk/Gv/9w+vi5YwFg0lJZUYuLfS/+ObmWE1sOsO87R7p1H0+IgyVyuSP+YY74/7bK22Q0cjQtg6qqKnr06NGkydmujhgDtTPJycl88MEHfPnll/j5+fHcc88xfPjwRonHVF/MhTPbOO8eS8yAcDxtr5TdaItSOH7oe1LdY5g4cy4vvnAv5pmH+XJHHIWGv7YiM5pMJCUlUVFRQWho6F9cRpG/RxRQO5Kens5bb73Fli1bcHd355VXXmHYsGGNSyHrK8jNOsXhKjcCIwcQ4GKBqb4GtV5LRXEGF84UUGPpjq2LO1EP3ktsiB+GxAJ0Dca/HEqn05Genn4tAyemsBuP6MK1E5mZmSxatIgffviByMhIXn/9dYYPH96o4k2jppiUU1/yzk8NREb2x7HmMpfyKsnLzkAaNoRwC0ssJQZO7fmRHz0FwswKyJHJ0fm5IZf99ZmZlZVFXl4e7u7uODo6itvRNAFRQO3ApUuXeP311/nmm28YOHAgzz//PPfcc0+jK59L0/ax6as9JF6s5/IvB/lRJtCAFU7hY5jVzw53z0FMf7oS+dovWbd0Nw1WfkQNn8rMKbF4mv1RQEajkaSkJAoLCwkLCxPdtyYiCugWc/HiRZYtW8aePXsYPHgwy5cvJzIysknLph2DRjP/hTuZpTdiEgSu7LYlQ2Fpj5OzJXIkdOs1lsfeHMDE+gaMUnNUdo442Vv85Qc3mUwkJiZSUFDAzJkzcXd3b83T7fSIArqFpKWl8e677/Ljjz8SExPDhx9+SGhoaJOPo7BwwMPzxiOFVKHC3kPFzTpaa7VacnNz0el0BAcHixOoTURMItwi0tLSWLp0KT/88ANDhgxh/fr1zRJPa5OXl0dJSQk+Pj64uLiI8U8TEUegNkan03H27FlWr17NoUOHGDNmDIsXL8bPz6+9TQOulA6VlpYSGBgoxj/NQBRQG3Pw4EHefvttkpKSGDNmDIsWLbotRp6r5ObmUlZWRp8+fXB2dm5vczocooDaiPr6ek6fPs2KFSu4cOEC999/P0uWLLm2eO124fLly5SVleHv7y+OQM1AjIHagPr6eg4cOMCCBQv45ZdfGDt2LM8///xtJx61Wk1eXh4APj4+YgPFZiCOQK2MRqPh4MGDvPPOO6SkpPDggw+ycOHC28ptu0pCQgLZ2dkEBQVda8go0jTEEagV0el07Nu3jzfffJOEhAQeeOABFi1aRGRkZHubdl2SkpLIyckhIiICLy+v9janQyKOQK1EXV0de/bs4b333iM7O5uHHnqIJ598koiIiPY27W/Jzc2lvLyc4OBgcQRqJqKAWgGNRsPevXtZvnw5ubm5zJgxgzlz5tw2qerrUV9fT15eHmZmZvj4+CCXi7dCcxCvWgupra3lwIEDLF++nIKCAmbMmMGTTz7ZrI2tbiVpaWlkZWURGBhIt27d2tucDosooBZQVVXFjh07eO+996irq+Mf//gHM2fOxMfHp71Nuyl5eXkUFxcTHBwszv+0ADGJ0Eyqqqr44osvWLZsGeXl5TzxxBM89thjHUI8giBw6dIlMjIyCA0N7RA2366IAmoGNTU1fPnll3zyySdotVrmzJnDI488gqenZ3ub1iiqqqpITU1Fq9Xi7u4uNlBsAaIL10QqKirYsWMHq1atutan+uGHH25Wn+r2oqCggLy8PLp3795hRH+7IgqoCZSXl7Np0yb+/e9/I5fLWbx4MY888kiHa8JRWFhIQUEBXl5eYv/rFiK6cI2krKyMDRs2sGbNGuRyOc899xxTp07tcOKBKz23c3NzCQoKEidQW4g4At0EQRAoLi5m06ZNbNq0CXNzc5555hkmT57cody2q+h0OrKzs6mqqsLHx0fMwLUQUUA3obCwkLVr17Jx40ZsbGx47rnnmDhxItbW1u1tWrPIyckhISEBBwcHvLy8xAnUFiK6cDegpKSE9evXs2bNGhQKBc899xyTJ0/usOKBK65oUVERPXr0ICgoqL3N6fCIAvob8vLy+PDDD1m/fj2enp688cYbjBkzpsP3jM7JySEtLY2wsDACAgLa25wOjzh+X4f09HTWr1/Ptm3bcHBwYMmSJY3sU31709DQQH5+PpWVlfj4+IgL6FoBUUB/IiMjg3fffZft27fj5eXFM888w+jRozvFZGN5eTnZ2dnY29vj4eEhNhBpBUQB/Y6cnBxWrFjBjh078PLyYvHixUyYMKHDu21XKSwsJCsrC3d3d7H/WyshCug3UlNTWblyJdu2bWPAgAHMmTOHvn37dhrxwBXXNC4ujpiYGLECu5UQBcSV0v4VK1awdetWevTowbPPPsuAAQMa3Wq3I2A0GsnPz6euro6AgAA8PDza26ROQZcXUGZmJitXrmT37t3ExsayZMkSBg0a1Onig8rKSnJycrC0tMTb27vDJ0RuF7qsgHQ6HefPn+ejjz5i//799O3bl6VLl9K7d+/2Nq1NKCoqupZAEOOf1qPLCujChQssXLiQc+fOMXr0aBYvXkxsbGx7m9VmlJSUkJ2dTffu3QkLC2tvczoNXW4i1Wg0cvToUd566y1OnDjBiBEjeO655zq1eOCKgHJycnBxcRH3QG1FutQIZDAYOHz4MP/61784efIk999/Py+88AIxMTHtbVqbotVqycnJwWg04uHh0aFLkW43uoyAdDodR44c4V//+hdnzpxhxIgRvPjii/Tq1au9TWtzioqKSEpKws3NjaCgoE6XIGlPuoQLp9frOX78OK+++irHjx9n2LBhvPTSS11CPHBlBWp8fDwODg54enoilXaJn/2W0OmvpMlk4tixY7z22mtcuHCBRx55pEuJB6C0tJS0tDS8vLwIDw9vb3M6FZ3ahdPr9Rw8eJBly5aRlJTEo48+yvz58wkMDGxv024Z9fX15ObmIpfL8ff3FxfQtTKdVkD19fUcOnSIf//736SnpzNx4kTmzp3bpcQDV9b/JCYm4ujoiI+Pjxj/tDKd0oWrr6/n2LFjvPHGG1y8eJFx48bxzDPPEBwc3N6m3XJqa2vJycnB2dmZ7t27i/FPK9PprqZareabb77hpZdeIj09nccff5yFCxd22dWXpaWlnDt3Dh8fH2JiYsQRqJVpUxfOWFdGUVEhlUZbnN1ccbZVItWXk1ekx9zWHgdb81ZVcG1tLTt27OD999+nsLCQxx9/nMcff/y271PdVhiNRioqKqivr8fe3h6VStXeJnU62nQEUuec48D6F3jquXf5eE8S5UagNp5dn2zh0LlMtK34XRUVFezcuZMPPviA8vJypk+f3mFa7bYV5eXlnD9/HicnJ0JCQjpVdfntQpsKyNI3lpFTxxNhkU/KqUuUVQO2EUS72+FhocfYSt9TXV3Nzp07Wb58OUVFRcycOZO5c+fi7+/fpX3+mpoaMjMzsba2xsvLq0tfi7aiTa+o3MoBt8hR3Bngh5euDq0RBH0JpuAw3Ny8aQ2HorKykq+++opVq1ZRWVnJrFmzeOyxx8R6L66MQFcnUIODg8URqA24BY8kBVYWGozmVdTqqkn49SI1ZlZYOdjT0nC2srKSL774gtWrV1NTU8OTTz7Jww8/LK625EpDyJKSEgoKCnB0dBSXMLQRt2AeSMDOzoCsto68S5co0TvhF+WDs3XL5FNWVsaXX37J2rVr0ev1zJo1ixkzZuDl5SVmmriSUElOTsbMzIyAgADMzc3b26ROyS0QkDlWVkoqsi5xXNGTyRP7EuBph6wF93hFRQWbN2/m/fffRyKR8NRTTzFt2jSxTdPvKCsrIz4+HhsbG6KiosQOpG3ELbiqKhzcI+huX4Us0I0g/27YtMBxLC0tZdOmTaxZswYzMzOeeeYZpk6dir29feuZ3AkoLS3lwoULWFtbEx4eLsY/bUTbCEhXQ25mCWWY4yrJILHKhj5PvERUmD9OZs0/bF5eHp9++inr169HoVCwaNEiJkyYIIrnT1yNf8rKyujVqxfdunUTM3BtRIsE9LexRv1lTv2wmY2/ahkQao5Hj0H08QvGWdn878rPz2f16tVs3LgRW1tbli5dyoMPPig2x7gOGo2GzMxMzM3N8ff3x8ysBU8tkRvSIgEJgnD9F5TWeIV5EVJQiGPQPdw1dCDeLbjP8/LyWLNmDRs3bsTBwYHFixczbdq0TtEttC1Qq9VkZGRgYWFBQEAACoWivU3qtDRZQBKJBL1ez8mTJ9m0aRPOzs64urpiZWWFj48Prq6uSCy86TPin8QONyGRyJBKm58xyMvLY9WqVXz66ac4Ozvz7LPPMnnyZFE8N0AU0K2jyQKSSqVotVqOHz/O+fPnUalUuLu7X5vtjoiIoGfPnkRERLR497PCwkJWr17N2rVr8fX15bXXXmPYsGHimv4bYDKZyM3NJSUlBXd3dwICAsT4pw1psoAEQcDc3JwBAwYQFRWFXq/n8uXLVFVV8b///Y9du3YRGBhIQEAAffr0YeDAgURFRTW5kLGgoIBVq1axbt06fH19WbZsGSNHjmyquV0OrVZLUlIS1dXVREVF4ejo2N4mdWqaLCCTyYRSqaRPnz7Mnz8fMzMzSkpKqKuru9Z7+cSJE3z33XccPnyYb7/9lhEjRjBp0iSCgoIalU7Nzc1l9erV7Nixg+joaBYvXsyIESOadYJdDa1WS1paGtbW1kRERKBUtiBz8xuCqQGdzoBEqkBhJueKRy5gMhjQ6xswAcgUmCnkyKUSwEiDvoEGg4BEYYa5XEZnndtuVhJBEASkUin29vbY2tpe67Pcv39/RowYQUpKChcvXiQ+Pp6DB6dXHLQAABFkSURBVA/y8ccfc+rUKUaPHs3YsWP/ttRGEARycnJ4/fXX2bt3Lz169OD5559n8ODBYnVBI/m9gKKiolosIF1NPueObGPXT0U4+N7F9MfvoZuFAqm6lPiDP/DV3lNUS0DiM4CxY8cxPNQKbcFJNn+9h9Npamwi7uWRcYOIcO+clRCtmoWTSqXXts646667KCws5L777mPz5s3s2bOHc+fOcezYMRYtWkTPnj3/8FmTycS5c+dYtmwZ33zzDQMHDuTll19mwIABLTGxy3FVQA4ODoSGhrZgAtVEdcEFtr6+lmN59fjeM5jQME8sZVIkgDqngMq8Enz69cVcEMDRDw9bOSZjKb8eyqVC342IXmbo1Kf5NccDV8dwnDthNr1NKxHc3d0ZN24c4eHhDB48mM8++4zt27eTm5vLU089xahRo7CysgKubL3x9ttv8+233zJ06FBRPM1Ar9eTkZFBZWUlACkpKXh4eGBlZdXEUh4jdcXn2bJsPXsqvJn02BgmjO+B1dWXawtIzU6j0DWWyROHYvc758BYdpI8lRN3THyQO/3kVOftZ2+qGl2tHhw7n4LavJRHIpEQGBiIq6srffv25ZtvvmHLli28+eab1NTUMG7cOFJSUlixYgU//fQTQ4YM4eWXX6Zfv35tbVqnQ61Wc+7cuWudSF988UVCQ0MZO3Ys99xzD05OTo1KaRvVZSRuX8uBUzXc8eQ0+sS4oKvUYG5viQzQFqeTeGIrm85qOZ58lmGTHuduPztUcsDcCYu6TIrTk0hRWFKdnYdG7oRE0Tlr8WSvvvrqq419s8lk4tSpU5w9e5bAwEAGDx7c6CpfpVJJt27diIiIwNLSklOnTvHrr79SXl7OF198wbFjx7jjjjt48cUX6d+/v1i71QzKysrYsGEDGRkZhISEIAgCCQkJnD59mri4OARBwM3NDaVSeYPUtom64gvs+Ggz8ebdcCiJ56c9+/n5ZAlOgT64OaiQKcyxcetOmJ815VnH2PJTEXKVF+Hd7VCYWWOlSWP/D1+ybfchzle60rdPX0I9VCg6YRh7ywR0FZVKRWhoKACHDx/m6NGjXL58mX79+l1LGIjzFs2joKCADz74AHNzc1asWMHkyZPx8PAgOTmZs2fPcvz4cTIzM3FxccHNze36DymhnvKU7/ngy1MIToO5d8rd9PDUkbtvN4fTIHBQFG62tji4d8cvtBdRYX7oLvxMfGYVDpG98VEpsHV2xM3Tl5DgCPr07k9vP1esOqN6aKe+cDY2NgQHB2Nvb09RURHTpk1j9uzZ9O7dW8y2NRODwUB2dja1tbV4eHgQHh5Ot27dCAoKYujQoezfv59t27axa9cucnJymDNnDiNHjrzOFpYGDFodDVa9GPnASO4dHY2tLhDr2hRe2HWYE5enE2yrxEICYIa9R1+mjo/njf8V8mtiBYNcHUHpQkiECyHtcB1uNbdcQIIgcPToUT766CNKSkqYNm0aCxcuJCIiQnTbWoBGoyEhIQGAPn36XEtf29raEhsbS3BwMAMHDuS///0v+/bt46WXXqKgoICHHnroTwW5UqQKFXYKS+w87DAHUDrTLaQvYcrDGLQCggC/X07s4OGCq7eevyuN7MzcUgGp1WpOnz7Nv//9b+Lj4xk1ahTPPPOMKJ5WQKvVkpmZCUB4ePhfRhZra2v69++Pq6srQUFBbN68mTfeeAO9Xs9jjz2GjY3NlTdKLFF1Cyfa5SBJF1IpjOmOr1RDbV45BstAAizNUPzBwzaQf7kaGxtbQoLtbs3J3kbcMgFpNBoOHjzIu+++S3JyMlOmTOGf//wnERERotvWCqjVai5evEhDQwMBAQHXnUCVy+UEBwczd+5cHB0deeedd1i3bh12dnZMmTLlN9FJUTmHMXhkMJ9+t5u9njKClVXEpxbgNHQqfTzlaItySM4rQWMUkOpriDsLFt0j6One9R6Ct0RAWq2WvXv3smLFChISEpg+fTpz5swRtxpsRcrKylCr1bi6uuLr63vDeR+VSsXMmTNRKBSsWLGC5cuXY2Njw7hx45DL5cgtnOg56gmmlq9gx85POGzWDa/eD/LPCXfgZFlP0i9H2brjELkaDSaLAHoNm8jEoeG4dsHcT5sLSKfTsWfPHpYvX05qaiozZszocjsktDUNDQ3ExcVhNBrp169fo1boKhQKpk+fTm1tLStWrOD999/Hy8vrWiLHwsGXOx9/k9j6BgyCDLmlCltLBSDHf/D9PNt7FCaTCUGiwFylQmUub3GXpY5Imwqourqaffv2sWbNGnJzc6+NPIGBgaLb1ooYDAaysrIwGo0EBQU1empBoVBw7733cubMGbZv3862bdvw9vbGzc0NJBIUlrbY/WXZlRQzSxUOlmKbYGjDvnA1NTV89913vPPOO2RkZDB16lTmzZsnbjHYBuj1euLj4zEYDPTs2bNJiw19fX2ZOnUqERER7N69m19++QW9Xt+G1nYu2kRAarWa7777jhUrVnD58mUefvhhnnzySQICAtri67o85eXlFBQUYGlp2eQ9gGQyGXfddRcPPvggarWab7/9lvz8/Da0tnPR6gLSaDR8++23LFu2jNzcXB577DFmz56Nn59fa3+VCFeqQy5evEh9fT3du3dv1lJ3pVLJyJEj8fHx4ciRI5w7d46GhoY2sLbz0aoCqqqqYuvWrbz33ntUVFQwb948nnjiiS69Q0JbYzQaOX36NA0NDURFRTVrubtEIiE0NJT+/ftTU1PD7t27KSwsbANrOx+tJqCamhq+/PJLVq5cSXl5ObNnz2bWrFlddm+eW4XRaOTChQvodDoCAgKa3WxFJpMxYcIEfHx8OHXqFCUlJa1saeekVQRUXV3Ntm3bWLVqFWq1mrlz5/KPf/zjSjZHpM0QBIHy8nIKCwuxtbXF09OzRS18o6Ki8PPzo6KigsTERDGZ0AhaJCCpVEpZWRlr167l3Xffpba2lvnz5/PYY4/h5OTUWjaK/A0Gg4Hk5GTUajUhISEtdpWlUum15SYnT56kvLy8lSy9/RAEgaSkJP7zn/+wcuXKZruszX5cXRXP559/zieffILJZGLx4sVMnz5dbLV7izAajaSmplJfX4+/v/91KqubhpmZGTExMXz33XekpqZSV1fXSpa2HQ0NDRQWFmI0GvH29m5STWVxcTGff/45SUlJxMXFcf/99zNkyJAm3b/NaqwokUioqqpizZo17Ny5E6VSyfz583n44YfFHRJuIUajkeTkZDQaDYGBgS3ulyeTyQgLC8PKyoqMjAzUanUrWdp21NTUsG7dOoqLi1mwYAHBwcGNSuNLJBIiIiJYunQpW7Zsudazo1+/fjzwwAP079+/UdezWW2t1Go1P/74IxUVFTg7O7N48WLGjx+PjY2NmP68RUilUjQaDSkpKej1+mvxT0uuv1QqvbZatbq6GrVafVv/nlKplJqaGk6cOEFWVhaTJk3Cx8en0XGgnZ0dY8aMISAggJ07d7Jr1y4+//xz4uLiGD9+PGPHjiUoKOiGnY2aJCCj0Uh2djbl5eXU1dUhl8vp378/EomE/fv3YzAYmnI4kRYgkUgoLS0lNTUVlUpFXFwc5eXlmEymZh9TJpNRWVlJcXExWq2W3bt3k5GRcdtWjsjlcoqLi8nJyUGj0XDkyBHy8/ObvKJZoVDg7OxMREQEmZmZnD17lqysLM6cOcMDDzzAvffei52d3XWvg0T42w7xf0WtVjN16lT27duHRCJBoVDg6uoq7n7WTmi1WkpLSzEzM8PR0bFVNtEyGo3XBOTs7IxKpbptBSSRSK41UAHw8vJqdhwok8kwGo3k5ORci/0kEglBQUHMnDmT+fPnX3eKoElXXC6Xc/fdd+Pp6XktWBME4e93aRBpU67Go9B6v0NbHLOtkMlkVFRUUFlZSUNDA9HR0bi6ujb5OFKpFKPRSGlpKXq9nrS0NGQyGY6OjkRGRjJkyJC/deOaJCCl0oxp06ah1WqbbKSISGsjk8m4fPkyWVlZ5OfnM2XKFGJjY5uUiZNIJNdWSm/bto2ysjLs7OwYOHAgEydOpH///gQFBf3t528iICP1FcWUlteiMYGduw/Ozs4IeiNys663+lDk9kMul9OtWzcMBgM+Pj74+vo2+rMmk4nCwkKOHz/Opk2byMzMxM3NjdGjRzNt2jRCQ0Nv2hr5hgIy1Fzi0Jb/svtwBqVSJdHjp9I3yB5jvSt9egZgby3uO9N+mKivKSK/sAqdAQSTAZMgQW5uRzdvT2zNb8+4pbVRKpWMGTOG2traG44U1+PChQu88cYb/Pzzz9ja2jJp0iQmTZpEQEBAo6djbiCgBtK++4r9mSpi/u8NhoVYkHfwHda/mY379LeItRTF066YDBQkfM/yVev5Ma4GBzdP7M0VKLBl5D9fZPJ9ITiZd34vwdramvHjxwM0aQsdk8lESUkJOp2O6Oho/vGPfzBkyJAmx1B/IyABKCPlQgUSSQw9ekbi2w1clDMpuHwEa197LDv/b3N7I1XgHjKcCUMPcjyxmMHTFjMxUkbm12+y5b9fEBK5kDsDHdqn8d8tRCqVNnnvqauf69evH6GhoUgkEhwdHZtViPs311cCSHHzgdyj8ez/NYWIscGoPPrQ514zjD4OiPppbyQoVSoczZW49LyLvnf1o3dgPVa53ak8lUlOfj0N/iDvgo0+GouNjc3/b+fVTG7wgHImZsxoojM2sPXTdagMjzJzfDje/WIBSdutBRdpJAL6ykwuHsqne8/76eWjwlgez6G4TAwO4dhZmSG9fTPQLceooyb3LHFpldQZpMgUChQY0TcYEJBiZu+CT1AI/o5WbXqv3kBAUhTeo1gwxwGn/3zEytfepqj+KWZP7ImPSox/2h8DDUU5HL6kQ2Oew697dtKQtZ8fsty5+9EZDAq3Q9mJ3QRtZT6H336ZjflS6hv0VOYkk17vQXi4Bxb6ErQuftwzZzlL+lu2aJPrm3EdAQkI9cXk6aQoLVxw6R7LlCefoLLiZTb8Zx3dvZ9nxp2+qMQhqH0xGqgtSyLb1hxyDrD2jSwMPncza8HbjOnriU1nVo+gQ1tdTJ7lQzz33jBc6s+z/V+vs91pDu+9NBrnktOcTU8BX5c2r6L4qwwEAU3RKY4knye1DpAqsAvoxdQZvXA25lFZXI2hM7sGHQSjroKkkymYR0/h+bdfZcbwINwiogkO74atUta5e7QZBZQWNsTOnkB0sDsKdQ25pS4MGNqHcA8H3D2jiY24m/4eCmRtfCGuM44IVOblkPDDz2RllFzZQFaqRVanQ+oSia+PI1ad+OHWUdBVJnE8AXr2jCI6MpaIXtEI2QWkX66m05f0ys2x8AinT5ANSkMVuZlpFKh6cGekL2YCKJ1c8AkJx10qafMHyXVcOB3lNTYoC3PJ3/sVG+Pk1OtLSTpVTY9R9xPr74oYAbU3NeScPMQFoy8TA71xkckQuocSUreDo3viiA0YQoB1Jx+FfkNfnUVadjLGnmMJ81G2+YjzZ/4iIAGwDBjKtEVDUCcd5+iZS5TJlTgN/yfTR8QS5CLKp90QBKhJYPcP37Dt4x3E1QRg/9MFogPt8fYLJCRYzZvbVoOklMenjaGHtwp5p1aRkZrMeFKSKvEZ1x1PZduPOH/mLwKSSCwJCLJEIgECutHjXhNIJCCVi3MK7Y4AmDBhR8CQyQTKzJHbyzEYwMw+kL4PzuQJx1RMFjIkAn/Zx6fzoaeyMIcMtRd3+3nSHtVLTVoPJCJyW6Er5ee1T7M6/W5eWDKFGI/mtfRqCeKYItLxEEyYdGoqEn9l38+ZOIR1x9Hq1osH2mmPVBGRlqCvy+DMV5vY9M0B9v2ajrXpaz5xcOeViSG3fPJYdOFEOhxGXQWFyZdIyq9GLwAKFTZeEfQLdrrlcbooIBGRFiDGQCIiLUAUkIhICxAFJCLSAkQBiYi0AFFAIiIt4P8BFQedI2TeHIUAAAAASUVORK5CYII=)
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.
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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,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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,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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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)
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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,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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