geometry
AreConcyclic
test if four points are concyclic
Calling Sequence
Parameters
Description
Examples
AreConcyclic(P1, P2, P3, P4, cond)
P1, P2, P3, P4
-
four points
cond
(optional) name
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.
withgeometry:
pointP1,0,0,pointP2,2,0,pointP3,2,2:
pointP4,0,2,pointP5,1,7:
AreConcyclicP1,P2,P3,P4
true
AreConcyclicP1,P2,P3,P5
false
pointP5,a,b:
AreConcyclicP1,P2,P3,P5,cond
AreConcyclic: "unable to determine if 32/45*(a^2+b^2-2*a-2*b)/(a^2+b^2+1) is zero"
FAIL
32a2+b2−2a−2b45a2+b2+1=0
make necessary assumption
assumecond
See Also
geometry[IsOnCircle]
geometry[point]
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