The routine returns true if the point f or the list/set of points f is on circle c; false if it is not; and FAIL if it is unable to reach a conclusion.

In case of FAIL, if the third optional argument is given, the condition that makes f on circle c is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $\&\mathrm{and}\left(\mathrm{expr\_1}=0,...,\mathrm{expr\_n}=0\right)$ where expr, expr_i are Maple expressions.

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

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

$\mathrm{circle}\left(\mathrm{c1}\,x^2+y^2=1\,\left[x\,y\right]\right),\mathrm{circle}\left(\mathrm{c2}\,{\left(x-2\right)}^2+y^2=1\,\left[x\,y\right]\right),\mathrm{point}\left(A\,-1\,0\right)\:$

$\mathrm{IsOnCircle}\left(A\,\mathrm{c1}\right)$

$\mathrm{true}$

$\mathrm{IsOnCircle}\left(A\,\mathrm{c2}\right)$

$\mathrm{false}$

$\mathrm{point}\left(A\,a\,\frac{1}{2}\right),\mathrm{point}\left(B\,\frac{3}{5}\,b\right)\:$

$\mathrm{IsOnCircle}\left(\left\{A\,B\right\}\,\mathrm{c2}\,'\mathrm{cond}'\right)$

IsOnCircle:   "hint: the following conditions must be satisfied: {24/25+b^2 = 0, 13/4+a^2-4*a = 0}"

$\mathrm{FAIL}$

$\mathrm{cond}$

$\left(\frac{24}{25}+b^2=0\right)\&and\left(\frac{13}{4}+a^2-4a=0\right)$

$\mathrm{assume}\left(\mathrm{op}\left(\mathrm{cond}\right)\right)$

$\mathrm{IsOnCircle}\left(\left\{A\,B\right\}\,\mathrm{c2}\right)$

$\mathrm{true}$