Question

In fig, O is the centre of the circle, CA is tangent at A and CB is tangent at B drawn to the circle. If ∠ACB = 75°, then ∠AOB = ______ 

 

Options

• 75°

• 85°

• 95°

• 105°

Answer 1

In fig, O is the centre of the circle, CA is tangent at A and CB is tangent at B drawn to the circle. If ∠ACB = 75°, then ∠AOB = 105°.

Explanation:

∠OAC = ∠OBC = 90°​

∠OAC + ∠OBC + ∠ACB + ∠AOB = 360°​ ….. (sum of angles of a quadrilateral)

90°​​ + 90°​​ + 75°​​ + ∠AOB = 360°

∠AOB = 105°