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Putnam 1963 A6

Source: Putnam 1963

May 1, 2022
Putnamconicsellipsegeometry

Problem Statement

Let UU and VV be any two distinct points on an ellipse, let MM be the midpoint of the chord UVUV, and let ABAB and CDCD be any two other chords through MM. If the line UVUV meets the line ACAC in the point PP and the line BDBD in the point QQ, prove that MM is the midpoint of the segment PQ.PQ.
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