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Mathematics

In the given figure, PQ is a chord of a circle with center O and PT is the tangent at point P. If angle QPT = 60°, then find angle PRQ where R is a point on the circle.

In the given figure, PQ is a chord of a circle with center O and PT is the tangent at point P. If angle QPT = 60°, then find angle PRQ where R is a point on the circle. Model Paper 3, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

From figure,

In the given figure, PQ is a chord of a circle with center O and PT is the tangent at point P. If angle QPT = 60°, then find angle PRQ where R is a point on the circle. Model Paper 3, Concise Mathematics Solutions ICSE Class 10.

⇒ ∠QPT + ∠QPA = 180° [Linear pairs]

⇒ ∠QPA = 180° - 60° = 120°.

We know that,

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

∴ ∠PRQ = ∠QPA = 120°.

Hence, ∠PRQ = 120°.

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