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interior angle bisector of BC intersects the trisectors

Source: Vietnam TST 2002 for the 43th IMO, problem 1

June 26, 2005
geometryangle bisectorperpendicular bisectorgeometry unsolved

Problem Statement

Find all triangles ABCABC for which ∠ACB\angle ACB is acute and the interior angle bisector of BCBC intersects the trisectors (AX,(AY(AX, (AY of the angle ∠BAC\angle BAC in the points N,PN,P respectively, such that AB=NP=2DMAB=NP=2DM, where DD is the foot of the altitude from AA on BCBC and MM is the midpoint of the side BCBC.
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