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concyclic wanted, incircle related

Source: Switzerland - Swiss TST 2000 p13

February 19, 2020
geometryincircleConcyclic

Problem Statement

The incircle of a triangle ABCABC touches the sides AB,BC,CAAB,BC,CA at points D,E,FD,E,F respectively. Let PP be an internal point of triangle ABCABC such that the incircle of triangle ABPABP touches ABAB at DD and the sides APAP and BPBP at QQ and RR. Prove that the points E,F,R,QE,F,R,Q lie on a circle.
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