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geometry

 TangentLine
 find the tangents of a point with respect to a circle

 Calling Sequence TangentLine(obj, P, c, n)

Parameters

 obj - name P - point c - circle n - (optional) list of two names

Description

 • The routine finds the tangent line(s) of point P with respect to circle c
 • The output is obj which is assigned to a list of two lines (two tangent lines), or a line (one tangent line), or nothing (there is no tangent).
 • If the third optional argument is given and in case there exists two tangent lines, the names of the tangent lines are the two elements in the list.
 • For more details on the tangent, use detail.
 • The command with(geometry,TangentLine) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(A,1,1\right),\mathrm{circle}\left(c,{a}^{2}+{b}^{2}=1,\left[a,b\right]\right)$
 ${A}{,}{c}$ (1)
 > $\mathrm{TangentLine}\left(\mathrm{obj},A,c,\left[\mathrm{l1},\mathrm{l2}\right]\right)$
 $\left[{\mathrm{l1}}{,}{\mathrm{l2}}\right]$ (2)
 > $\mathrm{form}\left(\mathrm{l1}\right),\mathrm{Equation}\left(\mathrm{l1}\right)$
 ${\mathrm{line2d}}{,}{-}{1}{+}{a}{=}{0}$ (3)
 > $\mathrm{form}\left(\mathrm{l2}\right),\mathrm{Equation}\left(\mathrm{l2}\right)$
 ${\mathrm{line2d}}{,}{1}{-}{b}{=}{0}$ (4)