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Trapezoid and midpoints

Source: Dutch Mathematical Olympiad 2005

September 19, 2005

geometrytrapezoidratiosimilar triangles

Problem Statement

Let

ABCD

be a quadrilateral with

AB \parallel CD

,

AB > CD

. Prove that the line passing through

AC \cap BD

and

AD \cap BC

passes through the midpoints of

AB

and

CD

.

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