Question

In the figure above (not to scale), PQ is a tangent segment to the circle at P.If P,R,S and T are concyclic points, `angle QPR =40^@` and `PR=RQ` then find `angle PTS`.

A. `80^@`
B. `100^@`
C. `60^@`
D. `120^@`

Answer 1

Correct Answer - B

Given `PR =RQ and angle Q=40^@`
`rArr angle RPQ =angle Q`
`therefore angle RPQ =40^@`
In `angle PQR`,
`angle PRQ =180^@-(40^@+40^@)=100^@`.
We have, exterior angle of cyclic qudarilateralis equal to its interior opposite angle.
`therefore angle PTS =angle PRQ`
(`because PRST` "a cyclic quadrilateral")
`therefore angle PTS =100^@`.