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Prove that CD bisects QH

Source: Turkey, TST D2, P2

May 10, 2006
Eulergeometryangle bisectorpower of a pointradical axisgeometry proposed

Problem Statement

From a point QQ on a circle with diameter ABAB different from AA and BB, we draw a perpendicular to ABAB, QHQH, where HH lies on ABAB. The intersection points of the circle of diameter ABAB and the circle of center QQ and radius QHQH are CC and DD. Prove that CDCD bisects QHQH.
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