Difference between revisions of "2020 IMO Problems/Problem 1"
| Line 4: | Line 4: | ||
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. | ||
| − | + | == Video solution == | |
https://youtu.be/rWoA3wnXyP8 | https://youtu.be/rWoA3wnXyP8 | ||
Revision as of 23:18, 26 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.
