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Incenter is a point of disc given by circumcircle

Source: CAPS 2024 p3

July 4, 2024
geometryinternational competitionscircumcircleinteriorsamelengthsincenter

Problem Statement

Let ABCABC be a triangle and DD a point on its side BC.BC. Points E,FE, F lie on the lines AB,ACAB, AC beyond vertices B,C,B, C, respectively, such that BE=BDBE = BD and CF=CD.CF = CD. Let PP be a point such that DD is the incenter of triangle PEF.P EF. Prove that PP lies inside the circumcircle Ω\Omega of triangle ABCABC or on it.
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