The Line through the Incenter and Circumcenter

show:
inradii
circumradii

r

≈

1.65

DF

≈

1.05

GE

≈

2.59

r

2

≈

2.73

DF

×

GE

≈

2.73

A

B

C

I

O

D

E

F

G

Let ABC be a triangle with inradius

r

, incenter I, and circumcenter O. Let the line OI intersect the circumcircle at D and E and the incircle at F and G, with F closer to D than to E. Then

r

2

=DF×GE

.