MathDB
A geo shortlist is not a shortlist without a config

Source: RMM Extralist 2021 G4

September 18, 2023
geometryconfig geoRMM Shortlist

Problem Statement

Let ABCABC be an acute triangle, let HH and OO be its orthocentre and circumcentre, respectively, and let SS and TT be the feet of the altitudes from BB to ACAC and from CC to ABAB, respectively. Let MM be the midpoint of the segment STST, and let NN be the midpoint of the segment AHAH. The line through OO, parallel to BCBC, crosses the sides ACAC and ABAB at FF and GG, respectively. The line NGNG meets the circle BGOBGO again at KK, and the line NFNF meets the circle CFOCFO again at LL. Prove that the triangles BCMBCM and KLNKLN are similar.
Back to ProblemsView on AoPS