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Prove a parallelogram

Source: Indian RMO 1994 Problem 6

October 25, 2005
geometryparallelogram

Problem Statement

Let ACAC and BDBD be two chords of a circle with center OO such that they intersect at right angles inside the circle at the point MM. Suppose KK and LL are midpoints of the chords ABAB and CDCD respectively. Prove that OKMLOKML is a parallelogram.
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