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In the given figure,, BC is a diameter of circle and ∠BAO = 60∘ . Then, ∠ADC

Posted by Nakshatra Yadav 11 months ago

CBSE > Class 09 > Mathematics

1 answers

Nakshatra Yadav 11 months ago

Given: BC is a diameter of circle ∠BAO = 60° ...(1) In ∆OAB, OA = OB ∴ ∠OAB = ∠OBA = 60° (angles opposite to equal sides are equal) ...(2) Also, ∠AOC = ∠OAB + ∠OBA (exterior angle) ⇒ ∠AOC = 60° + 60° (From (2)) ⇒ ∠AOC = 120° ...(3) We know, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle. Thus, ∠AOC = 2∠ADC ⇒ 120° = 2∠ADC (From (3)) ⇒ ∠ADC = 60° Hence, ∠ADC = 60°.

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CBSE > Class 09 > Mathematics