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Relationship between the lengths of the diagonals AC and BD

Source: Austrian Mathematical Olympiad 1998, Part 2, D2, P3

June 29, 2011
geometryparallelogramratiogeometry proposed

Problem Statement

In a parallelogram ABCDABCD with the side ratio AB:BC=2:3AB : BC = 2 : \sqrt 3 the normal through DD to ACAC and the normal through CC to ABAB intersects in the point EE on the line ABAB. What is the relationship between the lengths of the diagonals ACAC and BDBD?
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