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Problem 5 of RMO 2007 (Regional Mathematical Olympiad-India)

Source: Cyclic Trapezium

September 13, 2009
geometrytrapezoidgeometry unsolvedez

Problem Statement

A trapezium ABCD ABCD, in which AB AB is parallel to CD CD, is inscribed in a circle with centre O O. Suppose the diagonals AC AC and BD BD of the trapezium intersect at M M, and OM \equal{} 2. (a) If ∠AMB \angle AMB is 60∘, 60^\circ , find, with proof, the difference between the lengths of the parallel sides. (b) If ∠AMD \angle AMD is 60∘, 60^\circ , find, with proof, the difference between the lengths of the parallel sides. [Weightage 17/100]
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