# 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.