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In the given figure, PQ is a chord of a ...

In the given figure, `PQ` is a chord of a circle with centre `O` and `PT` is a tangent. If `/_QPT=60^(@)`, find `/_PRQ`.

Text Solution

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Mark a point `M` in the alternate segment.
Join `MP` and `MQ`.
Then, `/_PMQ=/_QPT=60^(@)` [angles in the alternate segments]
Now, `/_PMQ+/_PRQ=180^(@)` [`:'PMQR` is cyclic quadrilateral]
`implies/_PRQ=180^(@)-/_PMQ=180^(@)-60^(@)=120^(@)`.
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