MathDB
JBMO Shortlist 2019 G5

Source:

September 12, 2020
geometry

Problem Statement

Let PP be a point in the interior of a triangle ABCABC. The lines AP,BPAP, BP and CPCP intersect again the circumcircles of the triangles PBC,PCAPBC, PCA and PABPAB at D,ED, E and FF respectively. Prove that PP is the orthocenter of the triangle DEFDEF if and only if PP is the incenter of the triangle ABCABC.
Proposed by Romania
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