MathDB

Incenter I is the mid point of DE [mixtilinear incircle]

Source: IMO Shortlist 1993, Spain 1

March 29, 2005

geometryincentercircumcircleratioIMO Shortlist

Problem Statement

Let

ABC

be a triangle, and

I

its incenter. Consider a circle which lies inside the circumcircle of triangle

ABC

and touches it, and which also touches the sides

CA

and

BC

of triangle

ABC

at the points

D

and

E

, respectively. Show that the point

I

is the midpoint of the segment

DE