Answer :

Given:


Consider ΔAOB


Here,


OA = OB (radius)


OBA = OAB = 60° (angles opposite to equal sides are equal)


By angle sum property


OBA + OAB + AOB = 180°


60° + 60° + AOB = 180°


AOB = 180° — 60° — 60° = 60°


Here,


BOC = BOA + AOC = 180°


60° + AOC = 180°


AOC = 180° – 60° = 120°


We know that,


AOC = 2× ADC


AOC = ADC


×120° = ADC


ADC = 60°


∴∠ADC = 60°

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