MathDB
angle bisector wanted, <PAB = <PCB =1/4 (<A+ < C)

Source: Ukrainian Geometry Olympiad 2020, X p4

April 27, 2020
geometryangle bisectorequal angles

Problem Statement

Inside triangle ABCABC, the point PP is chosen such that ∠PAB=∠PCB=14(∠A+∠C)\angle PAB = \angle PCB =\frac14 (\angle A+ \angle C). Let BLBL be the bisector of △ABC\vartriangle ABC. Line PLPL intersects the circumcircle of △APC\vartriangle APC at point QQ. Prove that the line QBQB is the bisector of ∠AQC\angle AQC.
Back to ProblemsView on AoPS