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geometry

  

circle

  

define a circle

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

circle(c, [A, B, C], n, 'centername'=m)

circle(c, [A, B], n, 'centername'=m)

circle(c, [A, rad], n, 'centername'=m)

circle(c, eqn, n, 'centername'=m)

Parameters

c

-

the name of the circle

A, B, C

-

three points

rad

-

a number which is the radius of the circle

eqn

-

the algebraic representation of the circle (i.e., a polynomial or an equation)

n

-

(optional) list of two names representing the names of the horizontal-axis and vertical-axis

'centername'=m

-

(optional) m is a name of the center of the circle to be created

Description

  

A circle is the set of all points in a plane that have the same distance from the center.

  

A circle c can be defined as follows:

• 

from three points A, B, C. The input is a list of three points.

• 

from the two endpoints of a diameter of the circle c. The input is a list of two points.

• 

from the center of c and its radius. The input is a list of two elements where the first element is a point, the second element is a number.

• 

from its internal representation eqn. The input is an equation or a polynomial. If the optional argument n is not given:

– 

if the two environment variables _EnvHorizontalName and _EnvVerticalName are assigned two names, these two names will be used as the names of the horizontal-axis and vertical-axis respectively.

– 

if not, Maple will prompt for input of the names of the axes.

  

To access the information relating to a circle c, use the following function calls:

form(c)

returns the form of the geometric object (i.e., circle2d if c is a circle).

center(c)

returns the name of the center of c.

radius(c)

returns the radius of c.

Equation(c)

returns the equation that represents the circle c.

HorizontalName(c)

returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.

VerticalName(c)

returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.

detail(c);

returns a detailed description of the given circle c.

• 

The command with(geometry,circle) allows the use of the abbreviated form of this command.

Examples

withgeometry:

_EnvHorizontalNamem:_EnvVerticalNamen:

define circle c1 from three distinct points:

circlec1,pointA,0,0,pointB,2,0,pointC,1,2,'centername'=O1:

centerc1,coordinatescenterc1

O1,1,34

(1)

radiusc1

1162516

(2)

Equationc1

m2+n22m32n=0

(3)

detailc1

name of the objectc1form of the objectcircle2dname of the centerO1coordinates of the center1,34radius of the circle251616equation of the circlem2+n22m32n=0

(4)

define circle c2 (which is the same as c1) from two end points of a diameter

pointM,HorizontalCoordO1radiusc1,VerticalCoordO1,pointN,HorizontalCoordO1+radiusc1,VerticalCoordO1:

circlec2,M,N:

Equationc2

m2+n22m32n=0

(5)

define circle c3 (which is the same as c1) from the center of the circle and its radius

circlec3,centerc1,radiusc1:

Equationc3

m2+n22m32n=0

(6)

define circle c4 (which is the same as c1) from its algebraic representation

circlec4,Equationc1,'centername'=O2:

centerc4,coordinatescenterc4

O2,1,34

(7)

radiusc4

1162516

(8)

areac1

2516π

(9)

See Also

geometry[Apollonius]

geometry[area]

geometry[AreOrthogonal]

geometry[AreTangent]

geometry[CircleOfSimilitude]

geometry[draw]

geometry[FindAngle]

geometry[HorizontalName]

geometry[intersection]

geometry[IsOnCircle]

geometry[objects]

geometry[Pole]

geometry[powerpc]

geometry[RadicalAxis]

geometry[RadicalCenter]

geometry[randpoint]

geometry[similitude]

geometry[TangentLine]

geometry[tangentpc]

geometry[VerticalName]

 


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