Question 111
Given a triangle $ABC$ such that $\angle B = 90^{\circ}$, denote by $k$ the circle with center on $BC$ that is tangent to $AC$. Denote by $T$ a point of tangency of $k$ and the tangent from $A$ to $k$ (different from $AC$). If $B'$ is the midpoint of $AC$ and $M$ the intersection of $BB'$ and $AT$, prove that $MB = MT$.