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Geometry Mathley 12.1 fixed ratio HQ/HD

Source:

June 7, 2020
ratioequal ratioorthocenterfixed

Problem Statement

Let ABCABC be an acute triangle with orthocenter HH, and PP a point interior to the triangle. Points D,E,FD,E,F are the reflections of PP about BC,CA,ABBC,CA,AB. If QQ is the intersection of HDHD and EFEF, prove that the ratio HQ/HDHQ/HD is independent of the choice of PP.
Luis González
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