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If PT is a tangent to a circle with cent...

If `PT` is a tangent to a circle with centre `O` and `PQ` is a chord of the circle such that `/_QPT=70^(@)`, then find the measure of `/_POQ`.

Text Solution

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Mark a point `R` in the alternate segment.
Join `RP` and `RQ`.
Then, `/_PRQ=/_QPT=70^(@)` [angles in the alternate segments]
`:. /_POQ=2/_PRQ=2xx70^(@)=140^(@)`. [`:'` angle subtended by an arc on the centre is double the angle subtended at any point on the remaining part of the circle.]
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