Excircle of APR at AP = excircle of PQB at PQ <==> S is...
Source: 4th German TST 2005, problem 2, by Arend Bayer
May 12, 2005
geometrycircumcircleangle bisectorgeometry proposed
Problem Statement
Let be a triangle satisfying . Let be an arbitrary point on the side (different from and ), and let the line meet the circumcircle of triangle at a point (apart from the point ).
Let the circumcircle of triangle meet the line at a point (apart from ), and let the circumcircle of triangle meet the line at a point (apart from ).
Prove that the excircle of triangle at the side is identical with the excircle of triangle at the side if and only if the point is the midpoint of the arc on the circumcircle of triangle .