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Three circles meet at a point

Source: Malaysian SST 2023 P6

August 27, 2023
geometry

Problem Statement

Given a cyclic quadrilateral ABCDABCD with circumcenter OO, let the circle (AOD)(AOD) intersect the segments ABAB, ACAC, DBDB, DCDC at PP, QQ, RR, SS respectively. Suppose XX is the reflection of DD about PQPQ and YY is the reflection of AA about RSRS.
Prove that the circles (AOD)(AOD), (BPX)(BPX), (CSY)(CSY) meet at a common point.
Proposed by Leia Mayssa & Ivan Chan Kai Chin
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