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midpoint of a radius is equidistant from parallel chords of another circle

Source: Sharygin 2005 finals 10.3

August 29, 2019
circlesChordsparalleldistancegeometry

Problem Statement

Two parallel chords ABAB and CDCD are drawn in a circle with center OO. Circles with diameters ABAB and CDCD intersect at point PP. Prove that the midpoint of the segment OPOP is equidistant from lines ABAB and CDCD.
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