एक वृत्त में, ABCD एक चक्रीय चतुर्भुज है। AC और BD एक दूसरे को P पर प्रतिच्छेदित करती हैं। यदि AB = AC और ∠BAC = 48° है, तो ADC की माप कितनी है?

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SSC CGL 2021 Tier-I (Held On : 12 April 2022 Shift 3)
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  1. 104°
  2. 112°
  3. 132°
  4. 114°

Answer (Detailed Solution Below)

Option 4 : 114°
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दिया गया है:

AB = AC और ∠BAC = 48°

प्रयुक्त अवधारणा:

एक चक्रीय चतुर्भुज के विपरीत कोणों का योग = 180°

गणना:

∠ABC = ∠ACB  [∵ AB = AC]

∠BAC + ∠ABC + ∠ACB = 180°

इसलिए, ∠ABC = ∠ACB = (180° - 48°)/2 = 132°/2 = 66°

साथ ही, ∠ADC + ∠ABC = 180°

⇒ ∠ADC + 66° = 180°

⇒ ∠ADC = 180° - 66° = 114°

∴ ∠ADC की माप 114° है। 

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