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Angle bisectors all the way through...

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October 21, 2010
geometryrectanglegeometric transformationreflectioncircumcircleangle bisectorgeometry unsolved

Problem Statement

A point PP lies on the internal angle bisector of ∠BAC\angle BAC of a triangle △ABC\triangle ABC. Point DD is the midpoint of BCBC and PDPD meets the external angle bisector of ∠BAC\angle BAC at point EE. If FF is the point such that PAEFPAEF is a rectangle then prove that PFPF bisects ∠BFC\angle BFC internally or externally.
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