The perpendicular bisector of the bisector
Source: Iran TST 2013:TST 3,Day 2,Problem 2
July 26, 2013
Asymptotegeometrycircumcircleangle bisectorperpendicular bisectorgeometry proposed
Problem Statement
In triangle , and are the angle bisector and the altitude of vertex , respectively. The perpendicular bisector of , intersects the semicircles with diameters and which are drawn outside triangle in and , respectively. Prove that the quadrilateral is concyclic.Proposed by Mahan Malihi