Question
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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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
⇒ 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।
Last updated on May 30, 2025
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