In a circle with centre

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

Problem

O

PQ

is a diameter. Points

R

and

S

lie on the circle on the same side of

PQ

such that

PR = RS

. Lines

PR, RQ,

and

PS

are drawn. (i) Prove that

\angle PRQ = 90^\circ

. (ii) If

\angle PRS = 34^\circ

, calculate

\angle POS

. (iii) Hence, determine

\angle RPS