Line, passing 2 ants, tangent to a fixed circle
Source: Saint Petersburg olympiad 2024, 9.3
September 21, 2024
geometry
Problem Statement
The triangle is inscribed in a circle. Two ants crawl out of points and at the same time. They crawl along the arc towards each other so that the product of the distances from them to point remains unchanged. Prove that during their movement (until the moment of meeting), the straight line passing through the ants touches some fixed circle.