Line through incentres is perpendicular to bisectrix of AEB
Source: Romanian TST 2011
April 4, 2012
geometrycircumcircleincenterperpendicular bisectorgeometric transformationangle bisector
Problem Statement
Let be a triangle such that . The perpendicular bisector of the side meets the side at the point , and the (interior) bisectrix of the angle meets the circumcircle at the point . Prove that the (interior) bisectrix of the angle and the line through the incentres of the triangles and are perpendicular.