MathDB

identities with triangle of excenters

Source: Korean Mathematical Olympiad 1994, Final Round P3 FKMO

July 21, 2018

geometryexcentersincentercircumradius

Problem Statement

In a triangle

ABC

I

and

O

are the incenter and circumcenter respectively,

A',B',C'

the excenters, and

O'

the circumcenter of

\triangle A'B'C'

. If

R

and

R'

are the circumradii of triangles

ABC

and

A'B'C'

, respectively, prove that: (i)

R'= 2R

(ii)

IO' = 2IO