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Online Geometry Problem 733: Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC. L is a line through the orthocenter H that cuts the sides at A1, B1, and C1. Lines A1A2, B1B2, and C1C2 are the reflection of L in sides BC, AC, and AB, respectively. Prove that A1A2, B1B2, and C1C2 are concurrent at a point P on the circumcircle O.

 Triangle, Orthocenter, Reflection, Circumcircle, Concurrency

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 731-740 | Triangles | Altitude | Orthocenter | Perpendicular lines | Circumcircle | Congruence | Reflection | Email | Solution / comment | By Antonio Gutierrez