circles intersection is midpoint of chord, 3 circles (2014 Kyiv City MO 11.4.1)
Source:
August 6, 2020
geometrycirclesmidoint
Problem Statement
Construct for the triangle a circle passing through the point and touching the line at the point , a circle passing through the point and touches the line at the point . The second intersection point of the circles and is denoted by . The intersection point of the line and the circumscribed circle is denoted by . Prove that is the midpoint of the segment .