The Line through the Incenter and Circumcenter

show:
inradii
circumradii

r

≈

1.65

DF

≈

1.05

GE

≈

2.59

2

r

≈

2.73

DF

×

GE

≈

2.73

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

2

r

=DF×GE

.