Question

In Figure 2, PQ is a chord of a circle with centre O and PT is a tangent. If Angle QPT = 60, find Angle PRQ

Answer 1

Answer. Given, PQ is a chord of a circle with center O. Also, ∠QPT = 60°. let x be the point on the tangent PT.

Now, ∠QPT + ∠QPX = 180°  [Linear pair]

⇒ ∠QPX = 180° - ∠QPT = 180° - 60° = 120°

Again, ∠QPX = ∠PRQ  [Alternate segment theorem]

⇒ ∠PRQ = 120°