In a circle with centre

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

P

, the arc

QR

subtends an angle of

(5y - 10)^{\circ}

at the centre and an angle of

(2y + 5)^{\circ}

at a point

S

on the circumference. (i) Find the value of

y

. (ii) Hence determine the measures of

\angle QPR

and

\angle QSR

. (iii) If

T

is any other point on the circle in the same segment as

S

, find the measure of

\angle QTR

and justify your answer.