In , . The perpendicular bisector of meets the circumcircle of again at (other than…

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

Problem

\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

). (i) Prove that

QS = RS

. (ii) Show that points

P, Q, R

and

S

are concyclic. (iii) Prove that

PS

is a diameter of the circumcircle of

\triangle PQR