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The Line through the Incenter and Circumcenter

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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
.
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