Question 110
A point $P$ (distinct from $B$ and $C$) is marked on the side $BC$ of a triangle $ABC$. Let $I_1$ and $I_2$ be the centers of the inscribed circles of the triangles $ABP$ and $APC$, respectively. The circumcircle of the triangle $I_1PI_2$ intersects the segment $BC$ at $P$ and $Q$.
Prove that $AB + QC = AC + QB$.
(A. Voidelevich)
Prove that $AB + QC = AC + QB$.
(A. Voidelevich)