Problem

Source: India TST 2023 Practice Test 1 P1

Tags: geometry, perpendicular bisector



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