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

Line 8: Line 8:
  
 
https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems]
 
https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems]
 +
 +
==See Also==
 +
 +
{{IMO box|year=2020|before=First Problem|num-a=2}}
 +
 +
[[Category:Olympiad Geometry Problems]]

Revision as of 11:32, 14 May 2021

Problem

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 $\overline{AB}$.

Video solution

https://youtu.be/rWoA3wnXyP8

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

See Also

2020 IMO (Problems) • Resources
Preceded by
First Problem
1 2 3 4 5 6 Followed by
Problem 2
All IMO Problems and Solutions