The Distances to the Incenter and Excenters from the Circumcenter

show:
inradii
circumradii

OI

≈

0.21

OA'

≈

1.38

OB'

≈

1.02

OC'

≈

1.19

R

≈

0.61

2

OI

+

2

OA'

+

2

OB'

+

2

OC'

≈

4.42

12

2

R

≈

4.42

Let ABC be a triangle with circumradius

R

, circumcenter O, and incenter I. Let A', B', and C' be the radii of the excircles opposite A, B, and C, respectively. Then

2

OI

+

2

OA'

+

2

OB'

+

2

OC'

=12

2

R

.