The Distance from the Circumcenter to an Excenter

​
OE
≈
8.36
R
≈
4.81
r
≈
4.85
2
OE
≈
69.89
2
R
+
2
R
r
≈
69.89
Let ABC be a triangle with circumcenter O and let E be the excenter of the excircle opposite A. Let
R
be the circumradius and
r
the exradius. Then
2
OE
=
2
R
+2Rr
.

Details

The statement of the theorem is in Problem 157. Distance from the Circumcenter to the Excenter.

External Links

Circumcircle (Wolfram MathWorld)
Circumradius (Wolfram MathWorld)
Excircles (Wolfram MathWorld)
Exradius (Wolfram MathWorld)

Permanent Citation

Jay Warendorff, Antonio Gutierrez
​
​"The Distance from the Circumcenter to an Excenter"​
​http://demonstrations.wolfram.com/TheDistanceFromTheCircumcenterToAnExcenter/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011