Question

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 $\angle$ QPT = ${50}^o$ then $\angle$ POQ = ?

(a) ${100}^o$ (b) ${90}^o$ (c) ${80}^o$ (d) ${75}^o$

Answer 1

Angle OPQ = 90°-50°=40°
OP=OQ ( radii of circle)
angleOPQ= angleOQP=40°
(equal opposite side have equal opposite angles)

angle POQ =180°- angle OQP- angle OPQ
= 180°-40°-40°=100°

option (A) 100° is correct answer