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.

AND:
OR:
NO:

Found problems: 2

2020 Francophone Mathematical Olympiad, 1
Tags: geometry , sharky-devil , spiral similarity , incircle
Let $ABC$ be an acute triangle with $AC>AB$, Let $DEF$ be the intouch triangle with $D \in (BC)$,$E \in (AC)$,$F \in (AB)$,, let $G$ be the intersecttion of the perpendicular from $D$ to $EF$ with $AB$, and $X=(ABC)\cap (AEF)$. Prove that $B,D,G$ and $X$ are concylic

2021 China Girls Math Olympiad, 2
Tags: geometry , sharky-devil , incenter
In acute triangle $ABC$ ($AB \neq AC$), $I$ is its incenter and $J$ is the $A$-excenter. $X, Y$ are on minor arcs $\widehat{AB}$ and $\widehat{AC}$ respectively such that $\angle{AXI}=\angle{AYJ}=90^{\circ}$. $K$ is on line $BC$ such that $KI=KJ$. Proof that line $AK$ bisects $\overline{XY}$.