Multiple choice

AB is a diameter of a circle with centre at O. DC is a chord such that DC || AB. If ∠BAC=30o, then find ∠ADC? O केंद्र वाले वृत्त का व्यासAB है। DC उसकी जीवा है और DC || AB यदि ∠BAC=30o हो तो ∠ADC का मान ज्ञात कीजिए?

  1. 120o

  2. 110o

  3. 115o

  4. 100o
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A Correct answer
Explanation

Since AB is a diameter, ∠ACB = 90° (angle in a semicircle). In ΔABC, ∠ABC = 180° - 90° - 30° = 60°. ABCD is a cyclic quadrilateral with DC || AB. Opposite angles in a cyclic quadrilateral sum to 180°, so ∠ADC = 180° - ∠ABC = 180° - 60° = 120°.

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