Distance between the Incenter and the Center of the Apollonius Circle

2 d	2 4 s - 14 4 r - 11 2 S - 128 3 R r 32 2 r
1.85005	1.85005

Let

X

1

and

X

970

be the incenter and the center of the Apollonius circle of the triangle

ABC

, respectively.

Let

d=

X

1

X

970



,

R

,

r

and

s

be the circumradius, inradius and semiperimeter of

ABC

, and

S=2ABC

.

Then

2

d

=

2

4

s

-14

4

r

-11

2

S

-128R

3

r

32

2

r

[1].

References

[1] C. Kimberling, "Part 1: Introduction and Centers X(1)–X(1000)," Encyclopedia of Triangle Centers—ETC. (May 26, 2022) faculty.evansville.edu/ck6/encyclopedia/ETC.html.

External Links

Apollonius Circle (Wolfram MathWorld)

Radical Circle of Three Circles

Permanent Citation

Minh Trinh Xuan

"Distance between the Incenter and the Center of the Apollonius Circle"
http://demonstrations.wolfram.com/DistanceBetweenTheIncenterAndTheCenterOfTheApolloniusCircle/
Wolfram Demonstrations Project
Published: May 27, 2022