# Difference between revisions of "2020 IMO Problems/Problem 1"

$\textbf{Problem 1}$. Consider the convex quadrilateral $ABCD$. The point $P$ is in the interior of $ABCD$. The following ratio equalities hold: $\[\angle PAD : \angle PBA : \angle DPA = 1 : 2 : 3 = \angle CBP : \angle BAP : \angle BPC\]$ Prove that the following three lines meet in a point: the internal bisectors of angles $\angle ADP$ and $\angle PCB$ and the perpendicular bisector of segment $AB$.

## Video solution

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