Problem of Apollonius

May 2010
1
0
Given two circles of different radii, and a point, find the circle which will be tangent to all three of these. A circle is tangent to a point if the point is on the solution circle. If you can reduce one of the circles to a point or line that would be great because I have the scripts for every other solution except this one >_<.

Thanks guys.
 

earboth

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Given two circles of different radii, and a point, find the circle which will be tangent to all three of these. A circle is tangent to a point if the point is on the solution circle. If you can reduce one of the circles to a point or line that would be great because I have the scripts for every other solution except this one >_<.

Thanks guys.
1. For the more general solution have a look here: Apollonius' Problem -- from Wolfram MathWorld

2. You can reduce a circle around \(\displaystyle M(x_M, y_M)\) to a point if you use the radius 0:

\(\displaystyle (x-x_M)^2+(y-y_M)^2=0\) will yield M.
 
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