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वृत्त

Question
CBSEHHIMAH10010490

आकृति 8 में, 5 सेमी त्रिज्या वाला O केंद्र का वृत्त है। T एक ऐसा बिंदु है कि OT = 13 सेमी है तथा OT वृत्त को बिंदु E पर काटती है। यदि AB बिंदु E पर वृत्त की स्पर्श रेखा है तो AB की लम्बाई ज्ञात कीजिए, जबकि TP तथा TQ वृत्त की दो स्पर्श रेखाएँ हैं। 
             

Solution
angle OPT space equals space 90 degree
हम ा र े space प ा स space ह ैै comma space OP space equals space 5 space cm comma space OT space equals space 13 space cm
आयत space म ें space increment OPT comma
space space space space space space space OP squared space plus space PT squared space equals space OT squared space space space space space space space space space........ left square bracket प ा इथ ा ग ो रस space थ ् य ो रम space
rightwards double arrow space left parenthesis 5 right parenthesis squared space plus space PT squared space equals space left parenthesis 13 right parenthesis squared
rightwards double arrow space PT squared space equals space 169 space minus space 25 space equals space 144 space cm squared
rightwards double arrow space PT space equals square root of 144 space equals space 12 space cm
space space space space space space OP space equals space OQ space equals OE space equals space 5 space cm
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space........ left square bracket व ृ त ् त space क ा space त ् र ि ज ् य ा
space space space space space space space ET space equals space OT space minus space OE space equals 13 space minus space 5 space equals space 8
म ा न ा comma space PA space equals straight x space cm comma space तब space AT space equals space left parenthesis 12 minus straight x right parenthesis space cm
PA space equals space AE space equals space straight x space cm space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space......... left square bracket ब ा हर ी space ब िं द ु space स े space ख ीं च ी space गई space स ् पर ् शर े ख ा ए ं
आयत space म ें space increment AET comma
space space space space space space space space AE squared space plus space ET squared space equals space AT squared space space space space space space space space space space space.......... left square bracket प ा इथ ा ग ो रस space थ ् य ो रम space
rightwards double arrow space straight x squared space plus space left parenthesis 8 right parenthesis squared space equals space left parenthesis 12 space minus space straight x right parenthesis squared
rightwards double arrow space straight x squared space plus space 64 space equals space 144 space plus space straight x squared space minus space 24 straight x
rightwards double arrow space 24 straight x space equals space 144 space minus space 64 space equals space 80
rightwards double arrow space straight x space equals space begin inline style 80 over 24 end style space equals space begin inline style fraction numerator 10 space over denominator 3 end fraction end style space cm
AB space equals space AE space plus space EB space equals space AE space plus space AE space equals space 2 AE space equals space 2 straight x
therefore space AB space equals space 2 left parenthesis begin inline style 10 over 3 end style right parenthesis space equals begin inline style 20 over 3 end style cm space equals 6 begin inline style 2 over 3 end style cm
और space 6.67 space cm space और space 6.6 with bar on top space cm