AreTangent - Maple Help

geometry

 AreTangent
 test if a line and a circle or two circles are tangent to each other

 Calling Sequence AreTangent(f, g)

Parameters

 f, g - line and circle or two circles

Description

 • The routine returns true if l1 and l2 are tangent to each other; false if they are not; and FAIL if it is unable to determine if l1 and l2 are tangent to each other.
 • In case of FAIL, if the third optional argument is given, the condition that makes l1 and l2 tangent to each other is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $\left(\mathrm{expr1}=0\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&or\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(\mathrm{expr2}=0\right)$ where $\mathrm{expr}$, $\mathrm{expr1}$, $\mathrm{expr2}$ are maple expressions.
 • The command with(geometry,AreTangent) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{_EnvHorizontalName}≔'x':$$\mathrm{_EnvVerticalName}≔'y':$
 > $\mathrm{circle}\left(\mathrm{c1},{x}^{2}+{y}^{2}=1\right),\mathrm{circle}\left(\mathrm{c2},{\left(x-2\right)}^{2}+{y}^{2}=1\right):$
 > $\mathrm{line}\left(l,2x+3y=0\right):$
 > $\mathrm{AreTangent}\left(\mathrm{c1},\mathrm{c2}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{AreTangent}\left(l,\mathrm{c1}\right)$
 ${\mathrm{false}}$ (2)