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: 1

2022 Kosovo National Mathematical Olympiad, 3
Let $\bigtriangleup ABC$ be a triangle and $D$ be a point in line $BC$ such that $AD$ bisects $\angle BAC$. Furthermore, let $F$ and $G$ be points on the circumcircle of $\bigtriangleup ABC$ and $E\neq D$ point in line $BC$ such that $AF=AE=AD=AG$. If $X$ and $Y$ are the feet of perpendiculars from $D$ to $EF$ and $EG,$ respectively. Prove that $XY\parallel AD$.
geometry parallelism simson