केंद्र O वाले एक वृत्त का व्यास AB है। AB के दोनों ओर वृत्त पर C और D दो बिंदु इस प्रकार हैं, कि ∠CAB = 52° और ∠ABD = 47° हैं। ∠CAD और ∠CBD के मापों में अंतर (डिग्री में) क्या है?

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SSC CGL 2021 Tier-I (Held On : 21 April 2022 Shift 2)
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  2. 15
  3. 10
  4. 20

Answer (Detailed Solution Below)

Option 3 : 10
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Detailed Solution

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दिया गया है:

∠CAB = 52° और ∠ABD = 47°

प्रयुक्त अवधारणा:

परिधि पर किसी भी बिंदु पर व्यास द्वारा बनाया गया कोण 90°के बराबर होता है

गणना:

F2 Savita SSC 7-9-22 D2

अवधारणा के अनुसार,

∠ACB = ∠ADB = 90°

इसलिए, ∠CBA = 180° - (90° + 52°)

⇒ 180° - 142°

⇒ 38°

इसी प्रकार,

∠BAD = 180° - (90° + 47°)

⇒ 180° - 137°

⇒ 43°

इसलिए, ∠CAD = 52° + 43°

⇒ 95°

∠CBD = 38° + 47°

⇒ 85°

अब,

∠CAD - ∠CBD = 95° - 85°

⇒ 10°

∴ ∠CAD और CBD के मापों के बीच का अंतर (डिग्री में) 10 है।

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