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.

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

$\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)\:$

$\mathrm{line}\left(\mathrm{l3}\,3^{\frac{1}{2}}a+b-3^{\frac{1}{2}}-2=0\,\left[a\,b\right]\right)\:$

$\mathrm{AreConcurrent}\left(\mathrm{l1}\,\mathrm{l2}\,\mathrm{l3}\right)$

$\mathrm{true}$

$\mathrm{line}\left(\mathrm{l4}\,\mathrm{sqrt}\left(3\right)b-2\mathrm{sqrt}\left(3\right)=11\,\left[a\,b\right]\right)\:$

$\mathrm{AreConcurrent}\left(\mathrm{l1}\,\mathrm{l2}\,\mathrm{l4}\right)$

$\mathrm{false}$

$\mathrm{line}\left(\mathrm{l5}\,mb+3^{\frac{1}{2}}a-2=0\,\left[a\,b\right]\right)\:$

$\mathrm{AreConcurrent}\left(\mathrm{l1}\,\mathrm{l2}\,\mathrm{l5}\,'\mathrm{cond}'\right)$

AreConcurrent:   "unable to determine if 6*3^(1/2)*m-6*3^(1/2)+9 is zero"

$\mathrm{FAIL}$

$\mathrm{cond}$

$6\sqrt{3}m-6\sqrt{3}+9=0$

$\mathrm{assume}\left(\mathrm{cond}\right)$

$\mathrm{AreConcurrent}\left(\mathrm{l1}\,\mathrm{l2}\,\mathrm{l5}\right)$

$\mathrm{true}$