IM0 2020 Problem 1!
Posted: Fri Oct 16, 2020 10:12 pm
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.
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.