Question 63
Let $ABC$ be a scalene and non-right triangle. Let $A'$ be the second intersection point of the median drawn from $A$ with the circumcircle of the triangle. Let the tangents to the circumcircle of $ABC$ at points $A$ and $A'$ intersect at $A''$. Similarly define points $B''$ and $C''$. Prove that $A''$, $B''$, $C''$ are collinear.