AreConcyclic - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

geometry

 AreConcyclic
 test if four points are concyclic

 Calling Sequence AreConcyclic(P1, P2, P3, P4, cond)

Parameters

 P1, P2, P3, P4 - four points cond - (optional) name

Description

 • The routine tests if the four given points P1, P2, P3, and P4 are concyclic, i.e., if they lie on the same circle. It returns true if they are; false if they are not; or FAIL if it is able to determine if they are concyclic.
 • If FAIL is returned, and the optional argument cond is given, the condition that makes the points concyclic is assigned to this argument.
 • The command with(geometry,concyclic) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(\mathrm{P1},0,0\right),\mathrm{point}\left(\mathrm{P2},2,0\right),\mathrm{point}\left(\mathrm{P3},2,2\right):$
 > $\mathrm{point}\left(\mathrm{P4},0,2\right),\mathrm{point}\left(\mathrm{P5},1,7\right):$
 > $\mathrm{AreConcyclic}\left(\mathrm{P1},\mathrm{P2},\mathrm{P3},\mathrm{P4}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{AreConcyclic}\left(\mathrm{P1},\mathrm{P2},\mathrm{P3},\mathrm{P5}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{point}\left(\mathrm{P5},a,b\right):$
 > $\mathrm{AreConcyclic}\left(\mathrm{P1},\mathrm{P2},\mathrm{P3},\mathrm{P5},'\mathrm{cond}'\right)$
 AreConcyclic:   "unable to determine if 32/45*(a^2+b^2-2*a-2*b)/(a^2+b^2+1) is zero"
 ${\mathrm{FAIL}}$ (3)
 > $\mathrm{cond}$
 $\frac{{32}{}\left({{a}}^{{2}}{+}{{b}}^{{2}}{-}{2}{}{a}{-}{2}{}{b}\right)}{{45}{}\left({{a}}^{{2}}{+}{{b}}^{{2}}{+}{1}\right)}{=}{0}$ (4)

make necessary assumption

 > $\mathrm{assume}\left(\mathrm{cond}\right)$
 > $\mathrm{AreConcyclic}\left(\mathrm{P1},\mathrm{P2},\mathrm{P3},\mathrm{P5}\right)$
 ${\mathrm{true}}$ (5)