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:

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

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{\_EnvHorizontalName}≔m\:$$\mathrm{\_EnvVerticalName}≔n\:$

$\mathrm{circle}\left(\mathrm{c1}\,\left[\mathrm{point}\left(A\,0\,0\right)\,\mathrm{point}\left(B\,2\,0\right)\,\mathrm{point}\left(C\,1\,2\right)\right]\,'\mathrm{centername}'=\mathrm{O1}\right)\:$

$\mathrm{center}\left(\mathrm{c1}\right),\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{c1}\right)\right)$

$\mathrm{O1},\left[1\,\frac{3}{4}\right]$

$\mathrm{radius}\left(\mathrm{c1}\right)$

$\frac{\sqrt{25}\sqrt{16}}{16}$

$\mathrm{Equation}\left(\mathrm{c1}\right)$

$m^2+n^2-2m-\frac{3}{2}n=0$

$\mathrm{detail}\left(\mathrm{c1}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{c1}\\ \text{form of the object}& \mathrm{circle2d}\\ \text{name of the center}& \mathrm{O1}\\ \text{coordinates of the center}& \left[1\,\frac{3}{4}\right]\\ \text{radius of the circle}& \frac{\sqrt{25}\sqrt{16}}{16}\\ \text{equation of the circle}& m^2+n^2-2m-\frac{3}{2}n=0\end{array}$

$\mathrm{point}\left(M\,\mathrm{HorizontalCoord}\left(\mathrm{O1}\right)-\mathrm{radius}\left(\mathrm{c1}\right)\,\mathrm{VerticalCoord}\left(\mathrm{O1}\right)\right),\mathrm{point}\left(N\,\mathrm{HorizontalCoord}\left(\mathrm{O1}\right)+\mathrm{radius}\left(\mathrm{c1}\right)\,\mathrm{VerticalCoord}\left(\mathrm{O1}\right)\right)\:$

$\mathrm{circle}\left(\mathrm{c2}\,\left[M\,N\right]\right)\:$

$\mathrm{Equation}\left(\mathrm{c2}\right)$

$m^2+n^2-2m-\frac{3}{2}n=0$

$\mathrm{circle}\left(\mathrm{c3}\,\left[\mathrm{center}\left(\mathrm{c1}\right)\,\mathrm{radius}\left(\mathrm{c1}\right)\right]\right)\:$

$\mathrm{Equation}\left(\mathrm{c3}\right)$

$m^2+n^2-2m-\frac{3}{2}n=0$

$\mathrm{circle}\left(\mathrm{c4}\,\mathrm{Equation}\left(\mathrm{c1}\right)\,'\mathrm{centername}'=\mathrm{O2}\right)\:$

$\mathrm{center}\left(\mathrm{c4}\right),\mathrm{coordinates}\left(\mathrm{center}\left(\mathrm{c4}\right)\right)$

$\mathrm{O2},\left[1\,\frac{3}{4}\right]$

$\mathrm{radius}\left(\mathrm{c4}\right)$

$\frac{\sqrt{25}\sqrt{16}}{16}$

$\mathrm{area}\left(\mathrm{c1}\right)$

$\frac{25\mathrm{\pi }}{16}$