 similitude - Maple Help

geometry

 similitude
 find the insimilitude and outsimilitude of two circles Calling Sequence similitude(obj, c1, c2) Parameters

 obj - name which is assigned the internal and external centers of similitude c1, c2 - two circles Description

 • 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. Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{_EnvHorizontalName}≔'x':$$\mathrm{_EnvVerticalName}≔'y':$
 > $\mathrm{circle}\left(\mathrm{c1},{x}^{2}+{y}^{2}=1\right),\mathrm{circle}\left(\mathrm{c2},\left[\mathrm{point}\left(A,3,3\right),4\right]\right):$
 > $\mathrm{circle}\left(\mathrm{c3},{\left(x-2\right)}^{2}+{y}^{2}=1\right):$
 > $\mathrm{similitude}\left(\mathrm{obj1},\mathrm{c1},\mathrm{c2}\right)$
 $\left[{\mathrm{in_similitude_of_c1_c2}}{,}{\mathrm{ex_similitude_of_c1_c2}}\right]$ (1)
 > $\mathrm{map}\left(\mathrm{coordinates},\mathrm{obj1}\right)$
 $\left[\left[\frac{{3}}{{5}}{,}\frac{{3}}{{5}}\right]{,}\left[{-1}{,}{-1}\right]\right]$ (2)
 > $\mathrm{similitude}\left(\mathrm{obj2},\mathrm{c1},\mathrm{c3},\left[M,N\right]\right)$
 similitude:   "hint: the external and internal centers of similitude are the same"
 $\left[{M}{,}{N}\right]$ (3)
 > $\mathrm{detail}\left(\mathrm{obj2}\right)$
 $\left[\begin{array}{ll}{\text{name of the object}}& {M}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{1}{,}{0}\right]\end{array}{,}\begin{array}{ll}{\text{name of the object}}& {N}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{1}{,}{0}\right]\end{array}\right]$ (4)