MathDB
equal area condition

Source:

June 17, 2008
geometryparallelogramratiogeometry proposed

Problem Statement

Points M,N M,N are taken on sides BC,CD BC,CD respectively of parallelogram ABCD ABCD. Let E\equal{}BD\cap AM, F\equal{}BD\cap AN. Diagonal BD BD cuts triangle AMN AMN into two parts. Prove that these two parts have equal area if and only if the point K K given by EK∥AD,FK∥AB EK\parallel{}AD, FK\parallel{}AB lies on segment MN MN.
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