Mathematics

Mathematics

Problem

In a circle with centre

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. a. (i) Prove that

\angle PRQ = 90^\circ

. b. (ii) If

\angle PRS = 34^\circ

, calculate

\angle POS

. c. (iii) Hence, determine

\angle RPS

."

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