MathDB

2

Part of 2014 EGMO

Problems(1)

Incentre of ABC, orthocentre of DEF,midpointof Arc collinear

Source: European Girls’ Mathematical Olympiad - DAY 1 - P2

4/12/2014
Let DD and EE be points in the interiors of sides ABAB and ACAC, respectively, of a triangle ABCABC, such that DB=BC=CEDB = BC = CE. Let the lines CDCD and BEBE meet at FF. Prove that the incentre II of triangle ABCABC, the orthocentre HH of triangle DEFDEF and the midpoint MM of the arc BACBAC of the circumcircle of triangle ABCABC are collinear.
incentercircumcirclereflectionhomothetyInversionEGMOEGMO 2014