MathDB

Two circles in the plane do not intersect and do not lie inside each other. 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 the segments

A_1A_2

and

B_1B_2

, and

C

be the intersection point of these segments. Prove that the orthocenter of the triangle

ABC

belongs to a fixed line that does not depend on the choice of diameters.

Problem Statement