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cyclic wanted, circumcircle and another circle related

Source: 2021 Sharygin Finals grades X-XI p3

August 1, 2021
geometryConcyclicCyclic

Problem Statement

The bisector of angle AA of triangle ABCABC (AB>ACAB > AC) meets its circumcircle at point PP. The perpendicular to ACAC from CC meets the bisector of angle AA at point KK. A cừcle with center PP and radius PKPK meets the minor arc PAPA of the circumcircle at point DD. Prove that the quadrilateral ABDCABDC is circumscribed.
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