Question 115
Let $ABC$ be a triangle and $\Omega$ its circumcircle. Let $A'$ be the point diametrically opposite to $A$ on the circle $\Omega$. Let $I$ be the centre of the incircle of triangle $ABC$, and $E$ and $F$ the points of tangency of the incircle with the sides $AC$ and $AB$ respectively. The circumcircle of triangle $AEF$ meets the circle $\Omega$ again at the point $X$. Show that the points $A'$, $I$ and $X$ are collinear.