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Pseudo-incenter of a convex polygon

Source: Austrian-Polish 1985, Problem 9

July 5, 2015
combinatorial geometrygeometryextremal principlepolygon

Problem Statement

We are given a convex polygon. Show that one can find a point QQ inside the polygon and three vertices A1,A2,A3A_1,A_2,A_3 (not necessarily consecutive) such that each ray AiQA_iQ (i=1,2,3i=1,2,3) makes acute angles with the two sides emanating from AiA_i.
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