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geom3d

 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 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(geom3d,AreConcurrent) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,\left[0,0,0\right]\right),\mathrm{point}\left(B,\left[0,0,1\right]\right),\mathrm{point}\left(C,\left[0,1,0\right]\right),\mathrm{point}\left(F,\left[1,0,0\right]\right)$
 ${A}{,}{B}{,}{C}{,}{F}$ (1)
 > $\mathrm{line}\left(\mathrm{AB},\left[A,B\right]\right):$$\mathrm{line}\left(\mathrm{AC},\left[A,C\right]\right):$$\mathrm{line}\left(\mathrm{AF},\left[A,F\right]\right):$$\mathrm{line}\left(\mathrm{BC},\left[B,C\right]\right):$
 > $\mathrm{AreConcurrent}\left(\mathrm{AB},\mathrm{AC},\mathrm{AF}\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{AreConcurrent}\left(\mathrm{AB},\mathrm{AC},\mathrm{BC}\right)$
 ${\mathrm{false}}$ (3)