Mathematics

Mathematics

Problem

In

\triangle PQR

,

\angle PQR = \angle PRQ

. The perpendicular bisector of

QR

meets the circumcircle of

\triangle PQR

again at

S

(other than

Q

and

R

). a. (i) Prove that

QS = RS

. b. (ii) Show that points

P, Q, R

and

S

are concyclic. c. (iii) Prove that

PS

is a diameter of the circumcircle of

\triangle PQR

.

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