Answer :

Given: and


We know that,


AOB = 2× ACB


AOB = ACB


×90° = ACB


ACB = 45°


Now, consider ΔABC


By angle sum property


ACB + ABC + CAB = 180°


45° + 30° + CAB = 180°


CAB = 180° — 45° — 30° = 105°


Consider ΔAOB


Here,


OA = OB (radius)


Let OA = OB = x


By angle sum property


AOB + OAB + OBA = 180°


90° + x + x = 180°


2x = 180° – 90° = 90°


x = 45°


Now,


CAB = BAO + CAO = 105°


CAO = 105° – 45° = 60°


CAO = 60°

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