Question 46
Let $ABC$ be a triangle with incenter $I$ and circumcircle $\Omega$. A point $X\ne A$ on $\Omega$ satisfies $AI=XI$. The incircle touches $AC$ and $AB$ at $E$ and $F$, respectively. Let $M_a,M_b,M_c$ be the midpoints of $BC,CA,AB$, respectively. Let $T$ be the intersection of lines $M_bF$ and $M_cE$, and let $S$ be the second intersection of $AT$ with $\Omega$. Prove that $X,M_a,S,T$ are concyclic.