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A hard problem (From Japan 2001)

Source: Japanese MO Finals 2001

May 24, 2010
conicshyperbolageometry unsolvedgeometry

Problem Statement

Suppose that ABCABC and PQRPQR are triangles such that A,PA,P are the midpoints of QR,BCQR,BC respectively, and QR,BCQR,BC are the bisectors of ∠BAC,∠QPR\angle BAC,\angle QPR. Prove that AB+AC=PQ+PRAB+AC=PQ+PR.
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