Question 101
Point $I_b$ is the $B$-excenter of triangle $ABC$. If we denote by $M$ the midpoint of arc $BC$ of the circumcircle of triangle $ABC$ (the one that does not contain vertex $A$), and $MI_b$ intersects the circumcircle of triangle $ABC$ at $T$, prove that $TI_b^2 = TB \times TC$.