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Odd points give concurrency of perpendicular bisectors

Source: India TST 2023 Practice Test 1 P1

July 9, 2023

geometryperpendicular bisector

Problem Statement

Let

ABC

be a triangle, and let

D

be the foot of the

A-

altitude. Points

P, Q

are chosen on

BC

such that

DP = DQ = DA

. Suppose

AP

and

AQ

intersect the circumcircle of

ABC

again at

X

and

Y

. Prove that the perpendicular bisectors of the lines

PX

QY

, and

BC

are concurrent.
Proposed by Pranjal Srivastava