MathDB
Three concurrent lines

Source: Nordic MC 2023 P4

April 21, 2023
geometry

Problem Statement

Let ABCABC be a triangle, and MM the midpoint of the side BCBC. Let EE and FF be points on the sides ACAC and ABAB, respectively, so that ME=MFME=MF. Let DD be the second intersection of the circumcircle of MEFMEF and the side BCBC. Consider the lines ℓD\ell_D, ℓE\ell_E and ℓF\ell_F through D,ED, E and FF, respectively, such that ℓD⊥BC\ell_D \perp BC, ℓE⊥AC\ell_E \perp AC and ℓF⊥AB\ell_F \perp AB. Show that ℓD,ℓE\ell_D, \ell_E and ℓF\ell_F are concurrent.
Back to ProblemsView on AoPS