Inequalities for an Exradius of a Triangle

​
2 R - r - 2
R(R - 2 r)
r
A
2 R - r + 2
R(R - 2 r)
2.31852
4.63735
6.01372
Let
r
A
be the exradius of triangle
ABC
for the excircle opposite
A
, and let
R
and
r
be the circumradius and inradius of
ABC
.
Then
2R-r-2
R(R-2r)
≤
r
A
≤2R-r+2
R(R-2r)
,
and similarly for
r
B
and
r
C
, the other two exradii.
You can drag the points.

External Links

Excircles (Wolfram MathWorld)
The Sum of the Trilinear Coordinates of a Point

Permanent Citation

Minh Trinh Xuan
​
​"Inequalities for an Exradius of a Triangle"​
​http://demonstrations.wolfram.com/InequalitiesForAnExradiusOfATriangle/​
​Wolfram Demonstrations Project​
​Published: May 27, 2022