MathDB

11

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

prove orthocenter for antipodal point

Source: Sharygin 2023 - P11 (Grade-8-10)

3/4/2023
Let HH be the orthocenter of an acute-angled triangle ABCABC; EE, FF be points on AB,ACAB, AC respectively, such that AEHFAEHF is a parallelogram; X,YX, Y be the common points of the line EFEF and the circumcircle ω\omega of triangle ABCABC; ZZ be the point of ω\omega opposite to AA. Prove that HH is the orthocenter of triangle XYZXYZ.
geometryothorcenterantipodeSharygin Geometry OlympiadSharygin 2023