MathDB
collinear wanted, altitudes , orthocenter, 2 circles with diameters

Source: 2016 NZOMC Camp Selections p6

January 10, 2021
geometrycollinearorthocenter

Problem Statement

Altitudes ADAD and BEBE of an acute triangle ABCABC intersect at HH. Let P≠EP \ne E be the point of tangency of the circle with radius HEHE centred at HH with its tangent line going through point CC, and let Q≠EQ \ne E be the point of tangency of the circle with radius BEBE centred at BB with its tangent line going through CC. Prove that the points D,PD, P and QQ are collinear.
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