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Locus of points symmetric to a fixed point about a chord.

Source:

December 7, 2010
geometryparallelogramrectangletrapezoidPythagorean Theoremperpendicular bisectorgeometry unsolved

Problem Statement

A fixed point AA inside a circle is given. Consider all chords XYXY of the circle such that ∠XAY\angle XAY is a right angle, and for all such chords construct the point MM symmetric to AA with respect to XYXY . Find the locus of points MM.
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