Question 87
Given two circles on the plane do not intersect. We choose diameters $A_1B_1$ and $A_2B_2$ of these circles such that the segments $A_1A_2$ and $B_1B_2$ intersect. Let $A$ and $B$ be the midpoints of segments $A_1A_2$ and $B_1B_2$, $C$ be its intersection point. Prove that the orthocenter of the triangle $ABC$ belongs to the fixed line that does not depend on the choice of the diameters.