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perpendicular segments

Source: Problem 1, Polish NO 1992

October 1, 2005
geometrycircumcirclegeometry solved

Problem Statement

Segments ACAC and BDBD meet at PP, and ∣PA∣=∣PD∣|PA| = |PD|, ∣PB∣=∣PC∣|PB| = |PC|. OO is the circumcenter of the triangle PABPAB. Show that OPOP and CDCD are perpendicular.
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