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equal segments wanted, circumcircle and angle bisector related

Source: 1995 ITAMO p4

January 28, 2020
geometrycircumcircleequal segmentsangle bisector

Problem Statement

An acute-angled triangle ABCABC is inscribed in a circle with center OO. The bisector of ∠A\angle A meets BCBC at DD, and the perpendicular to AOAO through DD meets the segment ACAC in a point PP. Show that AB=APAB = AP.
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