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

(Created page with "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 = ∠CB...")
 
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Prove that the following three lines meet in a point: the internal bisectors of angles ∠ADP and
 
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.
 
∠P CB and the perpendicular bisector of segment AB.
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=Video solution=
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https://youtu.be/rWoA3wnXyP8

Revision as of 00:17, 27 September 2020

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