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geometry

 IsOnCircle
 test if a point, a list, or set of points is on a circle

 Calling Sequence IsOnCircle(f, c, cond)

Parameters

 f - a point, a list or a set of points c - a circle cond - (optional) a name

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{circle}\left(\mathrm{c1},{x}^{2}+{y}^{2}=1,\left[x,y\right]\right),\mathrm{circle}\left(\mathrm{c2},{\left(x-2\right)}^{2}+{y}^{2}=1,\left[x,y\right]\right),\mathrm{point}\left(A,-1,0\right):$
 > $\mathrm{IsOnCircle}\left(A,\mathrm{c1}\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{IsOnCircle}\left(A,\mathrm{c2}\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{point}\left(A,a,\frac{1}{2}\right),\mathrm{point}\left(B,\frac{3}{5},b\right):$
 > $\mathrm{IsOnCircle}\left(\left\{A,B\right\},\mathrm{c2},'\mathrm{cond}'\right)$
 IsOnCircle:   "hint: the following conditions must be satisfied: {24/25+b^2 = 0, 13/4+a^2-4*a = 0}"
 ${\mathrm{FAIL}}$ (3)
 > $\mathrm{cond}$
 $\left(\frac{{24}}{{25}}{+}{{b}}^{{2}}{=}{0}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(\frac{{13}}{{4}}{+}{{a}}^{{2}}{-}{4}{}{a}{=}{0}\right)$ (4)
 > $\mathrm{assume}\left(\mathrm{op}\left(\mathrm{cond}\right)\right)$
 > $\mathrm{IsOnCircle}\left(\left\{A,B\right\},\mathrm{c2}\right)$
 ${\mathrm{true}}$ (5)