MathDB

G5

Part of 2019 JBMO Shortlist

Problems(1)

JBMO Shortlist 2019 G5

Source:

9/12/2020
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
geometry