MathDB
Inequality with areas

Source: Moldova 2007 IMO-BMO TST I problem 1

March 5, 2007
inequalitiesgeometrycircumcircletrigonometryfunctiontriangle inequalitygeometry proposed

Problem Statement

Let ABCABC be a triangle and M,N,PM,N,P be the midpoints of sides BC,CA,ABBC, CA, AB. The lines AM,BN,CPAM, BN, CP meet the circumcircle of ABCABC in the points A1,B1,C1A_{1}, B_{1}, C_{1}. Show that the area of triangle ABCABC is at most the sum of areas of triangles BCA1,CAB1,ABC1BCA_{1}, CAB_{1}, ABC_{1}.
Back to ProblemsView on AoPS