MathDB
AM = AF iff <BAC = 60^o

Source: Austria Beginners' Competition 2018 p2

February 24, 2020
geometryequal segmentsmidpointaltitude

Problem Statement

Let ABCABC be an acute-angled triangle, MM the midpoint of the side ACAC and FF the foot on ABAB of the altitude through the vertex CC. Prove that AM=AFAM = AF holds if and only if ∠BAC=60o\angle BAC = 60^o.
(Karl Czakler)
Back to ProblemsView on AoPS