MathDB
all possible D for any choice of line l lie on a single circle.

Source: Tournament of Towns, Senior O- Level Paper, Spring 2020 , p5

June 4, 2020
geometrycirclesLocus

Problem Statement

Given are two circles which intersect at points PP and QQ. Consider an arbitrary line \ell through QQ, let the second points of intersection of this line with the circles be AA and BB respectively. Let CC be the point of intersection of the tangents to the circles in those points. Let DD be the intersection of the line ABAB and the bisector of the angle CPQCPQ. Prove that all possible DD for any choice of \ell lie on a single circle.
Alexey Zaslavsky