MathDB
JBMO Shortlist 2019 G6

Source:

September 12, 2020
geometryincenter

Problem Statement

Let ABCABC be a non-isosceles triangle with incenter II. Let DD be a point on the segment BCBC such that the circumcircle of BIDBID intersects the segment ABAB at E≠BE\neq B, and the circumcircle of CIDCID intersects the segment ACAC at F≠CF\neq C. The circumcircle of DEFDEF intersects ABAB and ACAC at the second points MM and NN respectively. Let PP be the point of intersection of IBIB and DEDE, and let QQ be the point of intersection of ICIC and DFDF. Prove that the three lines EN,FMEN, FM and PQPQ are parallel.
Proposed by Saudi Arabia
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