Let $\mathrm{c1}=A\left(a\right)$ and $\mathrm{c2}=B\left(b\right)$ be two nonconcentric circles and let I and E divide SensedMagnitude(AB) internally and externally in the ratio a/b. Then I and E are called the internal and the external centers of similitude of the two circles c1 and c2

The routine assigns to obj a list of two elements where the first element is the internal center of similitude, and then second element the external center of similitude.

For a detailed description of the centers of similitude obj, use the routine detail (i.e., detail(obj))

The command with(geometry,similitude) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{\_EnvHorizontalName}≔'x'\:$$\mathrm{\_EnvVerticalName}≔'y'\:$

$\mathrm{circle}\left(\mathrm{c1}\,x^2+y^2=1\right),\mathrm{circle}\left(\mathrm{c2}\,\left[\mathrm{point}\left(A\,3\,3\right)\,4\right]\right)\:$

$\mathrm{circle}\left(\mathrm{c3}\,{\left(x-2\right)}^2+y^2=1\right)\:$

$\mathrm{similitude}\left(\mathrm{obj1}\,\mathrm{c1}\,\mathrm{c2}\right)$

$\left[\mathrm{in\_similitude\_of\_c1\_c2}\,\mathrm{ex\_similitude\_of\_c1\_c2}\right]$

$\mathrm{map}\left(\mathrm{coordinates}\,\mathrm{obj1}\right)$

$\left[\left[\frac{3}{5}\,\frac{3}{5}\right]\,\left[\mathrm{-1}\,\mathrm{-1}\right]\right]$

$\mathrm{similitude}\left(\mathrm{obj2}\,\mathrm{c1}\,\mathrm{c3}\,\left[M\,N\right]\right)$

similitude:   "hint: the external and internal centers of similitude are the same"

$\left[M\,N\right]$

$\mathrm{detail}\left(\mathrm{obj2}\right)$

$\left[\begin{array}{ll}\text{name of the object}& M\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[1\,0\right]\end{array}\,\begin{array}{ll}\text{name of the object}& N\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[1\,0\right]\end{array}\right]$