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CentroAmerican 2015 #5

Source: 2015 CentroAmerican Math Olympiad #5

June 27, 2015
OMCCgeometryangle bisector

Problem Statement

Let ABCABC be a triangle such that AC=2ABAC=2AB. Let DD be the point of intersection of the angle bisector of the angle CABCAB with BCBC. Let FF be the point of intersection of the line parallel to ABAB passing through CC with the perpendicular line to ADAD passing through AA. Prove that FDFD passes through the midpoint of ACAC.
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