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danube senior parallel wanted 2018 P3

Source: Danube 2018 P3

December 11, 2018
geometryparallelangle bisectorcircumcircleperpendicular bisector

Problem Statement

Let ABCABC be an acute non isosceles triangle. The angle bisector of angle AA meets again the circumcircle of the triangle ABCABC in DD. Let OO be the circumcenter of the triangle ABCABC. The angle bisectors of ∠AOB\angle AOB, and ∠AOC\angle AOC meet the circle γ\gamma of diameter ADAD in PP and QQ respectively. The line PQPQ meets the perpendicular bisector of ADAD in RR. Prove that AR//BCAR // BC.
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