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A rectangle of center O

Source: RMO 2008, Grade 7, Problem 4

April 30, 2008
geometryrectangletrigonometrygeometric transformationrotationhomothetyanalytic geometry

Problem Statement

Let ABCD ABCD be a rectangle with center O O, AB≠BC AB\neq BC. The perpendicular from O O to BD BD cuts the lines AB AB and BC BC in E E and F F respectively. Let M,N M,N be the midpoints of the segments CD,AD CD,AD respectively. Prove that FM⊥EN FM \perp EN.
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