Question 56
Let $ABC$ be a triangle. Let $t$ be the tangent in $A$ to the circumscribed circle of the triangle $ABC$. We note $A'$ the point of $t$ so that the line $(BC)$ cuts the segment $[AA']$ in the middle. We note $C'$ the symmetric of $C$ compared to $t$. Show that points $B$, $A$, $C'$ and $A'$ are cocyclic.