In figure PQ is a chord of a circle with center O and PT is the tangent. If angle QPT = 60° , find angle PRQ. ( Class 10)

Question

In the figure, PQ is a chord of a circle with centre O and PT is the tangent. If angle QPT = 60°, find angle PRQ. (Class 10)

Answer 1

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°

Comments

What is Alternate Segment Theorem?

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The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment.