MathDB
Mixtilinear circle

Source: Kürschák 2004, problem 1

July 13, 2014
geometrycircumcirclegeometry unsolved

Problem Statement

Given is a triangle ABCABC, its circumcircle ω\omega, and a circle kk that touches ω\omega from the outside, and also touches rays ABAB and ACAC in PP and QQ, respectively. Prove that the AA-excenter of ABC\triangle ABC is the midpoint of PQ\overline{PQ}.