Geometry Problem 1253

Elements: Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency

In a triangle ABC, H is the orthocenter (see the figure below). Lines DEF and GJK are perpendicular at H so that G and F are on AB, D and K on BC, E and J on AC. Prove that the circumcircles of triangles EHJ, FHG, and DHK meet at a point P.


Geometry Problem 1253: Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency