Question

P,Q,R,S,T are points on a circle with centre O so that $\angle$PTQ= 2 x $\angle$RTS and PQ %undefined RS. Find $\angle$SOQ, if P,O,Q are in a straight line

• A. 45^o
• B. 90 ^o
• C. 60 ^o
• D. 30 ^o

Answer 1

The correct option is A 45^o

$\angle$PTQ= 90 (angle in a semi circle)

, hence $\angle$RTS = 45.

$\angle$ROS = 90 ( Inscribed angle= 2 *Angle at circumference)

OR=OS=OR (radius)

$\angle$RSO = $\angle$SOQ= 45${}^{\circ }$ (interior alternate angles)

Option (a)