MathDB
AFED is cyclic iff A-median meets EF on the circumcircle

Source: BMO Shortlist 2011, Saudi Arabia

April 9, 2012
geometrycircumcircleratiogeometry proposed

Problem Statement

Given a triangle ABCABC, let DD be the midpoint of the side ACAC and let MM be the point that divides the segment BDBD in the ratio 1/21/2; that is, MB/MD=1/2MB/MD=1/2. The rays AMAM and CMCM meet the sides BCBC and ABAB at points EE and FF, respectively. Assume the two rays perpendicular: AM⊥CMAM\perp CM. Show that the quadrangle AFEDAFED is cyclic if and only if the median from AA in triangle ABCABC meets the line EFEF at a point situated on the circle ABCABC.
Back to ProblemsView on AoPS