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AreConcyclic

  

test if four points are concyclic

 

Calling Sequence

Parameters

Description

Examples

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

withgeometry:

pointP1,0,0,pointP2,2,0,pointP3,2,2:

pointP4,0,2,pointP5,1,7:

AreConcyclicP1,P2,P3,P4

true

(1)

AreConcyclicP1,P2,P3,P5

false

(2)

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

(3)

cond

3245a2+b22a2ba2+b2+1=0

(4)

make necessary assumption

assumecond

AreConcyclicP1,P2,P3,P5

true

(5)

See Also

geometry[IsOnCircle]

geometry[point]

 


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