equilateral triangle(0,6, v) draws an equilateral triangle whose rst two vertices are at (0, 0)
and (6,0); the third vertex is calculated to be at (3,3*√3) and these coordinates are stored in the CAS variable
v. In CAS view, entering v returns point(3*(√3*i+1)), which is equal to (3,3*√3).
exbisector
Given three points that dene a triangle, creates the bisector of the exterior angles of the triangle whose
common vertex is at the rst point. The triangle does not have to be drawn in the Plot view.
exbisector(point1, point2, point3)
Examples:
exbisector(A,B,C) draws the bisector of the exterior angles of ΔABC whose common vertex is at point
A.
exbisector(0,–4i,4) draws the line given by y=x.
extract_measure
Returns the denition of a geometric object. For a point, that denition consists of the coordinates of the
point. For other objects, the denition mirrors their denition in Symbolic view, with the coordinates of their
dening points supplied.
extract_measure(Var)
harmonic_conjugate
Returns the harmonic conjugate of 3 points. Specically, returns the harmonic conjugate of point3 with
respect to point1 and point2. Also accepts three parallel or concurrent lines; in this case, it returns the
equation of the harmonic conjugate line.
harmonic_conjugate(point1, point2, point3) or harmonic_conjugate(line1,
line2, line3)
Example:
harmonic_conjugate(point(0, 0), point(3, 0), point(4, 0)) returns point(12/5, 0)
harmonic_division
Returns the harmonic conjugate of 3 points. Specically, returns the harmonic conjugate of point3 with
respect to point1 and point2 and stores the result in the variable var. Also accepts three parallel or concurrent
lines; in this case, it returns the equation of the harmonic conjugate line.
harmonic_division(point1, point2, point3, var) or harmonic_division(line1,
line2, line3, var)
Example:
harmonic_division(point(0, 0), point(3, 0), point(4, 0), p) returns point(12/5, 0)
and stores it in the variable p
206 Chapter 9 Geometry
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