MathDB

1

Part of 2020 Indonesia MO

Problems(1)

Circles centred on sides leading to a bisection

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

10/13/2020
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}.
geometrycircles2020bisectorIndonesia MOIndonesian MO