Let $M{}$ be the midpoint of the side $BC$ of the triangle $ABC$. The circle $\omega$ passes through $A{}$, touches the line $BC$ at $M{}$, intersects the side $AB$ at the point $D{}$ and the side $AC$ at the point $E{}$. Let $X{}$ and $Y{}$ be the midpoints of $BE$ and $CD$ respectively. Prove that the circumcircle of the triangle $MXY$ touches $\omega$. Alexey Doledenok
Problem
Source: 42nd International Tournament of Towns, Senior A-Level P3, Spring 2021
Tags: geometry, circles, Tournament of Towns