Difference between revisions of "2020 IMO Problems/Problem 1"
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https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems] | https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems] | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2020|before=First Problem|num-a=2}} | ||
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| + | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 10:32, 14 May 2021
Problem
Consider the convex quadrilateral 
. The point 
is in the interior of . The following ratio equalities hold:
![\[\angle PAD : \angle PBA : \angle DPA = 1 : 2 : 3 = \angle CBP : \angle BAP : \angle BPC.\]](http://latex.artofproblemsolving.com/2/6/e/26e0fa91015e07f3f022d7b879a86c21313be9f1.png)
Prove that the following three lines meet in a point: the internal bisectors of angles 
and 
and the perpendicular bisector of segment 
.
Video solution
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 | ||
