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 =120degree, then find ∠OPQ.

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^o, then find ∠OPQ.

Answer 1

∠QOP + ∠POR = 180°

∠QOP + 120° = 180°

∠QOP = 180° - 120°

∠QOP = 60°

In ΔPOQ

∠QOP + ∠OPQ + ∠PQO = 180°

60° + ∠OPQ + 90° = 180°

150° + ∠OPQ = 180°

∠OPQ = 180° - 150°

∠OPQ = 30°