यदि RP और RQ केंद्र O वाले एक वृत्त की दो स्पर्श रेखाएँ हैं, जैसे कि POQ = 120°, जहाँ P और Q वृत्त पर बिंदु हैं और R वृत्त के बाहर एक बिंदु है, तो PRQ बराबर है:

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 2)
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  1. 90°
  2. 75°
  3. 60°
  4. 45°

Answer (Detailed Solution Below)

Option 3 : 60°
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दिया गया है:

RP और RQ एक वृत्त की दो स्पर्शरेखाएँ हैं।

∠POQ = 120°

प्रयुक्त अवधारणा:

स्पर्शरेखा स्पर्श बिंदु पर वृत्त की त्रिज्या के साथ समकोण बनाती है।

चतुर्भुज के सभी कोणों का योग = 360°

गणना:

   F2 SSC PriyaS 13-2-24 D27

आकृति में:

OP ⊥ PR और OQ ⊥ RQ

∠OPR = ∠OQR = 90°

चतुर्भुज POQR में, 

⇒ ∠OPR + ∠OQR + ∠POQ + ∠PRQ = 360

​ 90 + 90 + 120 + ∠PRQ = 360

⇒∠PRQ = (360 - 300) = 60°

∴ सही उत्तर 60° है।

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