WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Circles of Apollonius

​
radii:
blue circle
5
red circle
10
yellow circle
6
outside tangent:
blue circle
red circle
yellow circle
radius of new circle is:
3.89052
Apollonius' problem asks for the circle tangent to three given circles or lines. Finding a circle tangent to three circles is the most difficult form of this problem. The solution is obtained by solving three simultaneous equations,
2
(x-
x
1
)
+
2
(y-
y
1
)
-
2
(r±
r
1
)
=0
​​
2
(x-
x
2
)
+
2
(y-
y
2
)
-
2
(r±
r
2
)
=0
​​
2
(x-
x
3
)
+
2
(y-
y
3
)
-
2
(r±
r
3
)
=0
,
with at most eight solutions.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.