MathDB

a circle passes through two vertices of a triangle

Source: Russian 2007

August 28, 2007

geometryincentercircumcirclegeometric transformationhomothetygeometry proposed

Problem Statement

Given a triangle

ABC

. A circle passes through vertices

B

and

C

and intersects sides

AB

and

AC

at points

D

and

E

, respectively. Segments

CD

and

BE

intersect at point

O

. Denote the incenters of triangles

ADE

and

ODE

M

and

N

, respectiely. Prove that the midpoint of the smaller arc

DE

lies on line

MN