किसी वृत्त पर स्पर्शरेखाओं का एक युग्म खींचने के लिए, जो एक दूसरे से 75° के कोण पर झुकी हों, वृत्त की उन दो त्रिज्याओं के अंतिम बिंदुओं पर स्पर्शरेखाएँ खींचना आवश्यक है, जिनके बीच का कोण है-

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RRB ALP Previous Paper 2 (Held On: 9 Aug 2018 Shift 2)
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  1. 65°
  2. 75°
  3. 95°
  4. 105°

Answer (Detailed Solution Below)

Option 4 : 105°
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अवधारणा:

त्रिज्या संपर्क बिंदु पर स्पर्शरेखा के लंबवत होती है।

चतुर्भुज के सभी कोणों का योग = 360°

गणना:

F1 AbhishekP Madhuri 23.02.2022 D1

PA और PB बाहरी बिंदु P से वृत्त पर खींची गई स्पर्श रेखाएँ हैं।

OAP = ∠OBP = 90° (त्रिज्या संपर्क के बिंदु पर स्पर्श रेखा के लंबवत होती है)

अब, चतुर्भुज OAPB में,

∠APB + ∠OAP + ∠AOB + ∠OBP = 360° 

75° + 90° + ∠AOB + 90° = 360°

∠AOB = 105°

इस प्रकार, दो त्रिज्याओं, OA और OB के बीच का कोण 105° है।

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