AreConcurrent - Maple Help

geometry

 AreConcurrent
 test if three lines are concurrent

 Calling Sequence AreConcurrent(l1, l2, l3, cond)

Parameters

 l1, l2, l3 - three lines cond - (optional) name

Description

 • Three straight lines l1, l2, and l3 are said to be concurrent if they lie in a plane and pass through a common point.
 • The routine returns true if l1, l2, and l3 are concurrent; false if they are not; and FAIL if it is unable to determine if the three lines are concurrent.
 • In case of FAIL, if the optional fourth argument cond is given, the condition that makes the lines concurrent is assigned to this argument.
 • The command with(geometry,AreConcurrent) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{line}\left(\mathrm{l1},3b-6=0,\left[a,b\right]\right):$$\mathrm{line}\left(\mathrm{l2},-{3}^{\frac{1}{2}}a+b+{3}^{\frac{1}{2}}-2=0,\left[a,b\right]\right):$
 > $\mathrm{line}\left(\mathrm{l3},{3}^{\frac{1}{2}}a+b-{3}^{\frac{1}{2}}-2=0,\left[a,b\right]\right):$
 > $\mathrm{AreConcurrent}\left(\mathrm{l1},\mathrm{l2},\mathrm{l3}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{line}\left(\mathrm{l4},\mathrm{sqrt}\left(3\right)b-2\mathrm{sqrt}\left(3\right)=11,\left[a,b\right]\right):$
 > $\mathrm{AreConcurrent}\left(\mathrm{l1},\mathrm{l2},\mathrm{l4}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{line}\left(\mathrm{l5},mb+{3}^{\frac{1}{2}}a-2=0,\left[a,b\right]\right):$
 > $\mathrm{AreConcurrent}\left(\mathrm{l1},\mathrm{l2},\mathrm{l5},'\mathrm{cond}'\right)$
 AreConcurrent:   "unable to determine if 6*3^(1/2)*m-6*3^(1/2)+9 is zero"
 ${\mathrm{FAIL}}$ (3)
 > $\mathrm{cond}$
 ${6}{}\sqrt{{3}}{}{m}{-}{6}{}\sqrt{{3}}{+}{9}{=}{0}$ (4)

make necessary assumption:

 > $\mathrm{assume}\left(\mathrm{cond}\right)$
 > $\mathrm{AreConcurrent}\left(\mathrm{l1},\mathrm{l2},\mathrm{l5}\right)$
 ${\mathrm{true}}$ (5)