Comprehension

निर्देश: निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें:

एक त्रिभुज ABC वृत्त x2 + y2 = 100 में अंकित है। B और C के निर्देशांक क्रमशः (6, 8) और (-8, 6) हैं।

BAC किसके बराबर है?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. π/2
  2. π/3 या 2π/3
  3. π/4 या 3π/4
  4. π/6 या 5π/6

Answer (Detailed Solution Below)

Option 3 : π/4 या 3π/4
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व्याख्या:

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⇒ BC = \(√{(6+8)^2+ (8-6)^2} =√200 = 10√2\)

मान लीजिये O वृत्त का केंद्र है

x2 +y2 = 100,

त्रिज्या = OB = OC = 10 इकाई

OB2 + OC2 = \(√{100+100} = 10√2\)

∆BOC में, OB2 + OC2 = BC2 = (10√2 )2

= 200

इसलिए ∠ BOC = 90° (पाइथागोरस प्रमेय के विलोम से)

तब, ∠ BAC = 45° या 180° - 45° = \(\frac{\pi}{4} या \frac{3\pi}{4}\) .. ((वृत्त के शेष भाग पर किसी बिंदु पर अंतरित कोण केंद्र पर अंतरित कोण का आधा होता है।)

∴ विकल्प (c) सही है।

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