Let D be the other point of intersection of the two circles. Therefore, all triangles BCD obtained when the direction of BC changes are similar. But DC is just a chord in a circle. And the longest chord is a diameter. B. A point P is selected on one of the circles on the outside arc.
P is projected through A and B to determine chord CD on another circle.
Prove that no matter where P is chosen on its arc, the length of the chord CD is always the same. Since the latter is fixed, so is the former. Alexander Bogomolny 2789506 .