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Circles centred on sides leading to a bisection

Source: Indonesian MO (INAMO) 2020, Day 1, Problem 1

October 13, 2020
geometrycircles2020bisectorIndonesia MOIndonesian MO

Problem Statement

Since this is already 3 PM (GMT +7) in Jakarta, might as well post the problem here.
Problem 1. Given an acute triangle ABCABC and the point DD on segment BCBC. Circle c1c_1 passes through A,DA, D and its centre lies on ACAC. Whereas circle c2c_2 passes through A,DA, D and its centre lies on ABAB. Let P≠AP \neq A be the intersection of c1c_1 with ABAB and Q≠AQ \neq A be the intersection of c2c_2 with ACAC. Prove that ADAD bisects ∠PDQ\angle{PDQ}.
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