Question
Download Solution PDFनिम्न आकृति में, B और D केंद्र वाले वृत्तों की त्रिज्याएँ क्रमशः 4 सेमी और x सेमी हैं। AC दोनों वृत्तों पर स्पर्श रेखा है। x का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
छोटे वृत्त की त्रिज्या (r) = 4 सेमी
AE = 6 सेमी; ईसी = 9 सेमी
प्रयुक्त अवधारणा:
स्पर्शरेखा संपर्क बिंदु पर वृत्त की त्रिज्या के साथ समकोण बनाती है।
शीर्ष सम्मुख कोण बराबर होता है।
गणना:
AD ⊥ AC तथा BC ⊥ AC
∠DAE = ∠BCE = 90°
△DAE तथा △BCE में
∠DAE = ∠BCE = 90°
∠AED = ∠BEC (शीर्ष कोण)
△DAE ∼ △BCE (AA समरूपता द्वारा)
C.P.C.T द्वारा
⇒ AE/EC = AD/BC
⇒ 6/9 = 4/BC
⇒ BC = 36/6 = 6 सेमी
∴ सही उत्तर 6 सेमी है।
Last updated on Jun 13, 2025
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