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center of square lies on angle bisector (2007 Estonia Open Junior 2.2)

Source:

March 27, 2020
geometryangle bisectorsquareright angle

Problem Statement

The center of square ABCDABCD is KK. The point PP is chosen such that P≠KP \ne K and the angle ∠APB\angle APB is right . Prove that the line PKPK bisects the angle between the lines APAP and BPBP.
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