Circles of Apollonius
Circles of Apollonius
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
2
(x-)
x
2
2
(y-)
y
2
2
(r±)
r
2
2
(x-)
x
3
2
(y-)
y
3
2
(r±)
r
3
with at most eight solutions.