This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2023 Indonesia Regional, 5
Tags: regional olympiad , geometry
Given $\triangle ABC$ and points $D$ and $E$ at the line $BC$, furthermore there are points $X$ and $Y$ inside $\triangle ABC$. Let $P$ be the intersection of line $AD$ and $XE$, and $Q$ be the intersection of line $AE$ and $YD$. If there exist a circle that passes through $X, Y, D, E$, and $$\angle BXE + \angle BCA = \angle CYD + \angle CBA = 180^{\circ}$$ Prove that the line $BP$, $CQ$, and the perpendicular bisector of $BC$ intersect at one point.