Question

PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that ∠POR = 120°. Find ∠OPQ.

Answer 1

∠POQ = 180° – 120° = 60°

In ∆OPQ, we know

∠POQ + ∠OQP + ∠OPQ = 180° ...(Sum of the angles of a ∆ is 180°)

60° + 90° + ∠OPQ = 180°

∠OPQ = 180° – 150° = 30°

∠OPQ = 30°