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192 Geometry
pole
Returns the pole of the given line with respect to the given
circle.
pole(circle, line)
Example:
pole(circle(x^2+y^2=1), line(x=3)) returns
point(1/3, 0)
powerpc
Given a circle and a point, returns the difference between the
square of the distance from the point to the circle’’s center and
the square of the circle’s radius.
powerpc(circle, point)
Example
powerpc(circle(point(0,0), point(1,1)-
point(0,0)), point(3,1)) returns 8
radical_axis
Returns the line whose points all have the same powerpc
values for the two given circles.
radical_axis(circle1, circle2)
Example:
radical_axis(circle(((x+2)²+y²) =
8),circle(((x-2)²+y²) = 8)) returns line(x=0)
reciprocation
Given a circle, returns the poles (points) of given polar lines
or the polar lines of given poles (points).
reciprocation(circle, point) or
reciprocation(circle, line) or
reciprocation(circle, list)
Example:
reciprocation(circle(x^2+y^2=1),{point(1/
3,0), line(x=2)}) returns [line(x=3), point(1/
2, 0)]