Question 10
Points $A_1$ and $B_1$ are marked on the sides $AC$ and $BC$ of a triangle $ABC$ so that $AA_1 + BB_1 = AB$. Let $I$ be incenter of the triangle $ABC$, and $O$ be circumcenter of the triangle $A_1B_1C$.
Prove that the lines $OI$ and $A_1B_1$ are perpendicular.
(I. Voronovich)
Prove that the lines $OI$ and $A_1B_1$ are perpendicular.
(I. Voronovich)