0

I'm interested in making a program that draws the [Apollonian gasket][1] fractal. For this, I need a way to find the radii of three mutually tangent Soddy circles given their centers, for example given circles $C_i$ with center $(x_i, y_i)$, I want to find their radii $r_i$. so that these circles are mutually tangent.

Thanks for your help.

zenzicubic
  • 453

1 Answers1

0

Hint : Let $p=r_A,q=r_B,r=r_C$ the resp radii you are looking for.

Let $a=BC,b=CA,c=AB.$

You just have to solve the following system of equations

$$\begin{cases}q+r&=&a\\p+r&=&b\\p+q&=&c\end{cases}.$$

Jean Marie
  • 88,997
  • It is to be noted that if we call $A',B',C'$ the points of tangency of these circles, the incircle of $ABC$ is the circumcenter of $A'B'C'$. – Jean Marie Apr 01 '23 at 18:18