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

Tags were heavily modified to better represent problems.

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Found problems: 2

2024 China Western Mathematical Olympiad, 3
Tags: geometry , tangent , isogonal , phantom point , similarity
$AB,AC$ are tangent to $\Omega$ at $B$ and $C$, respectively. $D,E,F$ lie on segments $BC,CA,AB$ such that $AF<AE$ and $\angle FDB= \angle EDC$. The circumcircle of $\triangle FEC$ intersects $\Omega$ at $G$ and $C$. Show that $ \angle AEF= \angle BGD$

2019 Polish MO Finals, 1
Tags: geometry , concyclic , orthocenter , tangent , phantom point
Let $ABC$ be an acute triangle. Points $X$ and $Y$ lie on the segments $AB$ and $AC$, respectively, such that $AX=AY$ and the segment $XY$ passes through the orthocenter of the triangle $ABC$. Lines tangent to the circumcircle of the triangle $AXY$ at points $X$ and $Y$ intersect at point $P$. Prove that points $A, B, C, P$ are concyclic.