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In the given figure, `O` is the centre of a circle and `PT` is the tangent to the circle. If `PQ` is a chord such that `/_QPT=50^(@)` then `/_POQ=?`

A

`100^(@)`

B

`90^(@)`

C

`80^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
Mark a point `R` in the alternate segment.
Join `PR` and `QR`.
Then, `/_PRQ=/_QPT=50^(@)` [angles in alternate segments]
Now, `/_POQ=2/_PRQ=100^(@)`
[`:'` angles at the centre is double the angle on the circle]
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