MathDB

cyclic ABCD, diagonals intersection, 2 incenters, isosceles wanted

Source: Danube 2015 Seniors P1

September 8, 2018

geometryisoscelescyclic quadrilateralincenter

Problem Statement

Let

ABCD

be a cyclic quadrangle, let the diagonals

AC

and

BD

cross at

O

, and let

I

and

J

be the incentres of the triangles

ABC

and

ABD

, respectively. The line

IJ

crosses the segments

OA

and

OB

M

and

N

, respectively. Prove that the triangle

OMN

is isosceles.