MathDB
DF divides the line segment EG into two equal parts

Source: Dutch IMO TST1 2011 p5

August 6, 2019
bisects segmentangle bisectorgeometry

Problem Statement

Let ABCABC be a triangle with ∣AB∣>∣BC∣|AB|> |BC|. Let DD be the midpoint of ACAC. Let EE be the intersection of the angular bisector of ∠ABC\angle ABC and the line ACAC. Let FF be the point on BEBE such that CFCF is perpendicular to BEBE. Finally, let GG be the intersection of CFCF and BDBD. Prove that DFDF divides the line segment EGEG into two equal parts.
Back to ProblemsView on AoPS