Question 62
In triangle $ABC$, the incircle touches sides $BC, CA, AB$ at $D, E, F$ respectively. Assume there exists a point $X$ on the line $EF$ such that
$$
\angle XBC = \angle XCB = 45^\circ.
$$
Let $M$ be the midpoint of the arc $BC$ on the circumcircle of $ABC$ not containing $A$.
Prove that $MD$ passes through $E$ or $F$.
$$
\angle XBC = \angle XCB = 45^\circ.
$$
Let $M$ be the midpoint of the arc $BC$ on the circumcircle of $ABC$ not containing $A$.
Prove that $MD$ passes through $E$ or $F$.