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Rombus ABCD, \angle AQO=\angle PBC

Source: 239 2011 J4

May 18, 2020
geometry

Problem Statement

Rombus ABCD with acute angle BB is given. OO is a circumcenter of ABCABC. Point PP lies on line OCOC beyond CC. PDPD intersect the line that goes through OO and parallel to ABAB at QQ. Prove that ∠AQO=∠PBC\angle AQO=\angle PBC.
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