Question 102
The excircle $\omega_A$ of a triangle $ABC$ touches the side $BC$ at $P$. Let $I_1$ be the center of the excircle of the triangle $ABP$ touching the side $BP$, and $I_2$ be the center of the excircle of the triangle $APC$ touching the side $PC$.
Prove that the circumcircle of the triangle $I_1I_2P$ touches the circle $\omega_A$.
(A. Voidelevich)
Prove that the circumcircle of the triangle $I_1I_2P$ touches the circle $\omega_A$.
(A. Voidelevich)