In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If $∠$ QPT = $60^{o}$ , find $∠$ PRQ.

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Solution

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°

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