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geom3d[RadicalPlane] - find the radical plane of two given spheres
geom3d[RadicalLine] - find the radical line of three given spheres
geom3d[RadicalCenter] - find the radical center of four given spheres
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Calling Sequence
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RadicalPlane(p1, s1, s2)
RadicalLine(p1, s1, s2, s3)
RadicalCenter(p1, s1, s2, s3, s4)
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Parameters
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p
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name
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s1, s2, s3, s4
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spheres
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Description
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The locus of points  which have the same power with respect to the two given spheres s1, s2 is a plane called radical plane.
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Let us introduce a third sphere s3. Now we have three radical planes that form a pencil whose axis is the straight line. This line is called the radical line of the three sphere.
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Now add a fourth sphere s4, and we have four radical lines. These four lines are clearly concurrent at the radical center.
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Examples
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Define two spheres s1, s2
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![sphere(s1, x^2+y^2+z^2 = 1, [x, y, z])](/support/helpjp/helpview.aspx?si=5944/file03989/math105.png)
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![sphere(s2, [point(B, [5, 5, 5]), 2])](/support/helpjp/helpview.aspx?si=5944/file03989/math109.png)
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Find the radical plane of s1 and s2
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![[10, 10, 10]](/support/helpjp/helpview.aspx?si=5944/file03989/math132.png)
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Simple check:
Generate a randpoint point on the radical plane:
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The power of point P with respect to two spheres s1 and s2 must be the same:
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Plotting:
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![draw([p, s1, s2], style = patchnogrid, orientation = [-26, 96], lightmodel = light1, title = `Radical plane of two given spheres`)](/support/helpjp/helpview.aspx?si=5944/file03989/math158.png)
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Find the radical line of three spheres:
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![sphere(s3, [point(A, 1, 2, 3), 3])](/support/helpjp/helpview.aspx?si=5944/file03989/math164.png)
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Warning, assume that the parameter in the parametric equations is _t
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Find the radical center of four given spheres:
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![sphere(s4, [point(A, -3, 7, 1), 3])](/support/helpjp/helpview.aspx?si=5944/file03989/math190.png)
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![[249/100, 471/100, 0]](/support/helpjp/helpview.aspx?si=5944/file03989/math214.png)
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