Question 31
Let $a$ and $b$ be two parallel lines. The circle $\Omega$ is tangent to the line $a$ at the point $A$ and intersects the line $b$ at the distinct points $B$ and $C$. The point $T$ lies on the line $a$. The lines $B T$ and $C T$ meet the circle $\Omega$ again at the points $M$ and $N$, respectively. Show that the line $M N$ bisects the segment $[A T]$.