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E, F, Z, Y are concyclic

Source: IMO Shortlist 1995, G3

May 31, 2008
geometrytrigonometryIMO Shortlistharmonic divisionpower of a pointincirclegeometry solved

Problem Statement

The incircle of triangle △ABC \triangle ABC touches the sides BC BC, CA CA, AB AB at D,E,F D, E, F respectively. X X is a point inside triangle of △ABC \triangle ABC such that the incircle of triangle △XBC \triangle XBC touches BC BC at D D, and touches CX CX and XB XB at Y Y and Z Z respectively. Show that E,F,Z,Y E, F, Z, Y are concyclic.
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