Question
Download Solution PDFकेंद्र O वाले एक वृत्त का व्यास AB है। यदि P वृत्त पर बिंदु इस प्रकार है कि ∠AOP = 110° है, तो ∠OBP का माप है:
Answer (Detailed Solution Below)
Detailed Solution
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केंद्र O वाले एक वृत्त का व्यास AB है। यदि P वृत्त पर बिंदु इस प्रकार है कि ∠AOP = 110° है,
प्रयुक्त सूत्र:
त्रिभुज के कोणों का योग = 180°
गणना:
आकृति के अनुसार,
⇒ OA = OP = OB = त्रिज्या
ΔOPB में
⇒ OP = OB
इसलिए, ∆OPB एक समद्विबाहु त्रिभुज है
⇒ ∠OPB = ∠OBP = x
जैसे, AB एक सरल रेखा है
⇒ ∠AOP + ∠POB = 180°
⇒ ∠POB = 180° - 110° = 70°
ΔOPB में ,
⇒ ∠O + ∠P + ∠B = 180°
⇒ 70° + x + x = 180°
⇒ 2x = 180° - 70° = 110°
⇒ x = 55°
⇒ इसलिए, ∠OBP का माप 55º है
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