|
geometry[circle] - define a circle
|
|
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
|
|
|
>
|
|
|
>
|
 
|
define circle c1 from three distinct points:
|
>
|
![circle(c1, [point(A, 0, 0), point(B, 2, 0), point(C, 1, 2)], 'centername' = O1)](/support/helpjp/helpview.aspx?si=5835/file04098/math220.png)
|
|
>
|
|
|
![O1, [1, 3/4]](/support/helpjp/helpview.aspx?si=5835/file04098/math227.png)
| (1) |
|
>
|
|
|
| (2) |
|
>
|
|
|
| (3) |
|
>
|
|
|
| (4) |
define circle  (which is the same as  ) from two end points of a diameter
|
>
|
|
|
>
|
![circle(c2, [M, N])](/support/helpjp/helpview.aspx?si=5835/file04098/math262.png)
|
|
>
|
|
|
| (5) |
define circle  (which is the same as  ) from the center of the circle and its radius
|
>
|
![circle(c3, [center(c1), radius(c1)])](/support/helpjp/helpview.aspx?si=5835/file04098/math279.png)
|
|
>
|
|
|
| (6) |
define circle  (which is the same as  ) from its algebraic representation
|
>
|
|
|
>
|
|
|
![O2, [1, 3/4]](/support/helpjp/helpview.aspx?si=5835/file04098/math303.png)
| (7) |
|
>
|
|
|
| (8) |
|
>
|
|
|
| (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]
|
|
