MathDB
Union of the triangular regions BAD,CBE,ACF covers ABC

Source: India tst 2006 p6

June 27, 2012
geometry unsolvedgeometry

Problem Statement

Let ABCABC be an equilateral triangle, and let D,ED,E and FF be points on BC,BABC,BA and ABAB respectively. Let ∠BAD=α,∠CBE=β\angle BAD= \alpha, \angle CBE=\beta and ∠ACF=γ\angle ACF =\gamma. Prove that if α+β+γ≥120∘\alpha+\beta+\gamma \geq 120^\circ, then the union of the triangular regions BAD,CBE,ACFBAD,CBE,ACF covers the triangle ABCABC.
Back to ProblemsView on AoPS