P,Q,R,S,T are points on a circle with centre O so that ∠PTQ= 2 x ∠RTS and PQ

Question

P,Q,R,S,T are points on a circle with centre O so that

∠

PTQ= 2 x

∠

RTS and PQ %undefined RS. Find

∠

SOQ, if P,O,Q are in a straight line

Options:

A . 45∘

B . 90∘

C . 60∘

D . 30∘

Answer: Option A
:
A

P,Q,R,S,T Are Points On A Circle With Centre O So That ∠PT...

∠

PTQ= 90 (angle in a semi circle)
, hence

∠

RTS = 45.

∠

ROS = 90 ( Inscribed angle= 2 *Angle at circumference)
OR=OS=OR (radius)

∠

RSO =

∠

SOQ= 45

^{\circ}

(interior alternate angles)
Option (a)

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