locus of circumcenters, circles tangent to fixed line intersecting fixed circle
Source: 2011 XIV All-Ukrainian Tournament of Young Mathematicians, Qualifying p5
May 18, 2021
geometryLocusCircumcenterfixedUkrainian TYM
Problem Statement
The circle touches the line at point A. Let be a given positive number. We consider various circles of radius that touch a line and have two different points in common with the circle . Let be the touchpoint of the circle with the line , and the points of intersection of the circles and are denoted by and (Assume that the distance from point to the line is greater than the distance from point to this line). Find the locus of the centers of the circumscribed circles of all such triangles .