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is ABC isosceles if AP = AQ ?, angle bisectors wtice

Source: TOT 560 1997 Autumn S A1 - Tournament of Towns

September 11, 2024
geometryisoscelesequal segmentsangle bisector

Problem Statement

MM and NN are the midpoints of the sides ABAB and ACAC of a triangle ABC respectively. PP and QQ are points on the sides ABAB and ACAC respectively such that the bisector of the angle ACBACB also bisects the angle MCPMCP, and the bisector of the angle ABCABC also bisects the angle NBQNBQ. If AP=AQAP = AQ, does it follow that ABCABC is isosceles?
(V Senderov)
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