Question 21
(FRA 4) A right-angled triangle $OAB$ has its right angle at the point $B$. An arbitrary circle with center on the line $OB$ is tangent to the line $OA$. Let $AT$ be the tangent to the circle different from $OA$ ($T$ is the point of tangency). Prove that the median from $B$ of the triangle $OAB$ intersects $AT$ at a point $M$ such that $MB=MT$.