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 IsRightTriangle
 test if a given triangle is a right triangle

 Calling Sequence IsRightTriangle(ABC, cond )

Parameters

 ABC - triangle cond - (optional) name

Description

 • 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.

Examples

 > with(geometry):
 > triangle(T, [2, 2, 3]);
 ${T}$ (1)
 > IsRightTriangle(T);
 ${\mathrm{false}}$ (2)
 > triangle(ABC, [point(A,0,0), point(B,2,0), point(C,0,2)]);
 ${\mathrm{ABC}}$ (3)
 > IsRightTriangle(ABC);
 ${\mathrm{true}}$ (4)
 > point(B,1,b):
 > IsRightTriangle(ABC,'cond');
 IsRightTriangle:   "hint: one of the following conditions must be satisfied: {-4*b = 0, 4*b-8 = 0, -2*b^2+4*b-2 = 0}"
 ${\mathrm{FAIL}}$ (5)
 > cond;
 ${\mathrm{&or}}{}\left({-}{4}{}{b}{=}{0}{,}{4}{}{b}{-}{8}{=}{0}{,}{-}{2}{}{{b}}^{{2}}{+}{4}{}{b}{-}{2}{=}{0}\right)$ (6)
 > assume(op(1,cond));
 > IsRightTriangle(ABC);
 ${\mathrm{true}}$ (7)