MathDB
midpoints, feet of altitudes and other midpoints, lead to concurrency

Source: Austrian Federal Competition For Advanced Students 2009, Part 1, p4

August 30, 2019
geometryaltitudesmidpointsconcurrencyconcurrent

Problem Statement

Let D,ED, E, and FF be respectively the midpoints of the sides BC,CABC, CA, and ABAB of △ABC\vartriangle ABC. Let Ha,Hb,HcH_a, H_b, H_c be the feet of perpendiculars from A,B,CA, B, C to the opposite sides, respectively. Let P,Q,RP, Q, R be the midpoints of the HbHc,HcHaH_bH_c, H_cH_a, and HaHbH_aH_b respectively. Prove that PD,QEPD, QE, and RFRF are concurrent.
Back to ProblemsView on AoPS