ITOT 42 Spring 2021 - THPT A - additive practice Question 3

Let $M$ be the midpoint of side $BC$ of triangle $ABC$. A circle $\omega$ through $A$ touches $BC$ at $M$ and meets $AB,AC$ again at $D,E$, respectively. Let $X,Y$ be the midpoints of $BE,CD$, respectively. Prove that the circumcircle of $MXY$ is tangent to $\omega$. (5 points)



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