 circle - Maple Help

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

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{_EnvHorizontalName}≔m:$$\mathrm{_EnvVerticalName}≔n:$

define circle c1 from three distinct points:

 > $\mathrm{circle}\left(\mathrm{c1},\left[\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,2,0\right),\mathrm{point}\left(C,1,2\right)\right],'\mathrm{centername}'=\mathrm{O1}\right):$
 > $\mathrm{center}\left(\mathrm{c1}\right),\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{c1}\right)\right)$
 ${\mathrm{O1}}{,}\left[{1}{,}\frac{{3}}{{4}}\right]$ (1)
 > $\mathrm{radius}\left(\mathrm{c1}\right)$
 $\frac{\sqrt{{25}}{}\sqrt{{16}}}{{16}}$ (2)
 > $\mathrm{Equation}\left(\mathrm{c1}\right)$
 ${{m}}^{{2}}{+}{{n}}^{{2}}{-}{2}{}{m}{-}\frac{{3}}{{2}}{}{n}{=}{0}$ (3)
 > $\mathrm{detail}\left(\mathrm{c1}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{c1}}\\ {\text{form of the object}}& {\mathrm{circle2d}}\\ {\text{name of the center}}& {\mathrm{O1}}\\ {\text{coordinates of the center}}& \left[{1}{,}\frac{{3}}{{4}}\right]\\ {\text{radius of the circle}}& \frac{\sqrt{{25}}{}\sqrt{{16}}}{{16}}\\ {\text{equation of the circle}}& {{m}}^{{2}}{+}{{n}}^{{2}}{-}{2}{}{m}{-}\frac{{3}}{{2}}{}{n}{=}{0}\end{array}$ (4)

define circle $\mathrm{c2}$ (which is the same as $\mathrm{c1}$) from two end points of a diameter

 > $\mathrm{point}\left(M,\mathrm{HorizontalCoord}\left(\mathrm{O1}\right)-\mathrm{radius}\left(\mathrm{c1}\right),\mathrm{VerticalCoord}\left(\mathrm{O1}\right)\right),\mathrm{point}\left(N,\mathrm{HorizontalCoord}\left(\mathrm{O1}\right)+\mathrm{radius}\left(\mathrm{c1}\right),\mathrm{VerticalCoord}\left(\mathrm{O1}\right)\right):$
 > $\mathrm{circle}\left(\mathrm{c2},\left[M,N\right]\right):$
 > $\mathrm{Equation}\left(\mathrm{c2}\right)$
 ${{m}}^{{2}}{+}{{n}}^{{2}}{-}{2}{}{m}{-}\frac{{3}}{{2}}{}{n}{=}{0}$ (5)

define circle $\mathrm{c3}$ (which is the same as $\mathrm{c1}$) from the center of the circle and its radius

 > $\mathrm{circle}\left(\mathrm{c3},\left[\mathrm{center}\left(\mathrm{c1}\right),\mathrm{radius}\left(\mathrm{c1}\right)\right]\right):$
 > $\mathrm{Equation}\left(\mathrm{c3}\right)$
 ${{m}}^{{2}}{+}{{n}}^{{2}}{-}{2}{}{m}{-}\frac{{3}}{{2}}{}{n}{=}{0}$ (6)

define circle $\mathrm{c4}$ (which is the same as $\mathrm{c1}$) from its algebraic representation

 > $\mathrm{circle}\left(\mathrm{c4},\mathrm{Equation}\left(\mathrm{c1}\right),'\mathrm{centername}'=\mathrm{O2}\right):$
 > $\mathrm{center}\left(\mathrm{c4}\right),\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{c4}\right)\right)$
 ${\mathrm{O2}}{,}\left[{1}{,}\frac{{3}}{{4}}\right]$ (7)
 > $\mathrm{radius}\left(\mathrm{c4}\right)$
 $\frac{\sqrt{{25}}{}\sqrt{{16}}}{{16}}$ (8)
 > $\mathrm{area}\left(\mathrm{c1}\right)$
 $\frac{{25}{}{\mathrm{\pi }}}{{16}}$ (9)