 AreConcyclic - Maple Help

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)