This routine tests if the given triangle ABC is a right triangle. It returns true if ABC is a right triangle; false if it is not; and FAIL if it is unable to reach a conclusion.

If FAIL is returned, and the optional argument is given, the condition that makes ABC a right triangle is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $\&\mathrm{or}\left(\mathrm{expr\_1}=0,\mathrm{expr\_2}=0,...,\mathrm{expr\_n}\right)$ where expr, expri_i are Maple expressions.

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

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

$\mathrm{triangle}\left(T\,\left[2\,2\,3\right]\right)$

$T$

$\mathrm{IsRightTriangle}\left(T\right)$

$\mathrm{false}$

$\mathrm{triangle}\left(\mathrm{ABC}\,\left[\mathrm{point}\left(A\,0\,0\right)\,\mathrm{point}\left(B\,2\,0\right)\,\mathrm{point}\left(C\,0\,2\right)\right]\right)$

$\mathrm{ABC}$

$\mathrm{IsRightTriangle}\left(\mathrm{ABC}\right)$

$\mathrm{true}$

$\mathrm{point}\left(B\,1\,b\right)\:$

$\mathrm{IsRightTriangle}\left(\mathrm{ABC}\,'\mathrm{cond}'\right)$

IsRightTriangle:   "hint: one of the following conditions must be satisfied: {-4*b = 0, 4*b-8 = 0, -2*b^2+4*b-2 = 0}"

$\mathrm{FAIL}$

$\mathrm{cond}$

$\mathrm{\&or}\left(-4b=0\,4b-8=0\,-2b^2+4b-2=0\right)$

$\mathrm{assume}\left(\mathrm{op}\left(1\,\mathrm{cond}\right)\right)$

$\mathrm{IsRightTriangle}\left(\mathrm{ABC}\right)$

$\mathrm{true}$