Difference between revisions of "2020 IMO Problems/Problem 1"
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− | + | == Problem == | |
− | <cmath>\angle PAD : \angle PBA : \angle DPA = 1 : 2 : 3 = \angle CBP : \angle BAP : \angle BPC</cmath> | + | Consider the convex quadrilateral <math>ABCD</math>. The point <math>P</math> is in the interior of <math>ABCD</math>. The following ratio equalities hold: |
− | Prove that the following three lines meet in a point: the internal bisectors of angles <math>\angle ADP</math> and | + | <cmath>\angle PAD : \angle PBA : \angle DPA = 1 : 2 : 3 = \angle CBP : \angle BAP : \angle BPC.</cmath> Prove that the following three lines meet in a point: the internal bisectors of angles <math>\angle ADP</math> and <math>\angle PCB</math> and the perpendicular bisector of segment <math>\overline{AB}</math>. |
− | <math>\angle PCB</math> and the perpendicular bisector of segment <math>AB</math>. | + | |
== Video solution == | == Video solution == | ||
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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] | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=2020|before=First Problem|num-a=2}} | ||
+ | |||
+ | [[Category:Olympiad Geometry Problems]] |
Latest revision as of 11:32, 14 May 2021
Problem
Consider the convex quadrilateral . The point is in the interior of . The following ratio equalities hold: 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 |