2020 IMO Problems/Problem 1

Problem 1. Consider the convex quadrilateral ABCD. The point P is in the interior of ABCD. The following ratio equalities hold: ∠P AD : ∠P BA : ∠DP A = 1 : 2 : 3 = ∠CBP : ∠BAP : ∠BP C. Prove that the following three lines meet in a point: the internal bisectors of angles ∠ADP and ∠P CB and the perpendicular bisector of segment AB.

Video solution

https://youtu.be/rWoA3wnXyP8 https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems]