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ukmj
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Say the points are (a,b,c),(a1,b1,c1),(a2,b2,c2).
ukmj said:Say the points are (a,b,c),(a1,b1,c1),(a2,b2,c2).
The center of a 3D circle can be found by using the formula:
(x,y,z) = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3, (z1 + z2 + z3)/3
Where (x1,y1,z1), (x2,y2,z2), and (x3,y3,z3) are the coordinates of the 3 given points.
The radius of a 3D circle can be calculated by finding the distance between any of the 3 points and the center of the circle. This can be done using the distance formula:
r = √[(x-xc)^2 + (y-yc)^2 + (z-zc)^2]
Where (xc,yc,zc) is the coordinates of the center point and (x,y,z) is the coordinates of any of the 3 given points.
No, the center of a 3D circle must lie within the triangle formed by the 3 given points. This is because the 3 points are the only points that lie on the circle's circumference, and the center must be equidistant from all points on the circumference.
If the 3 given points are collinear, it means they lie on the same line. In this case, there is no unique solution for the center and radius of the 3D circle. This is because any point on the line can be chosen as the center, and the radius would be equal to half the distance between any two of the given points.
Yes, if the 3 given points are all the same point, the 3D circle would have an infinite radius. This is because the distance between any point on the circle and the center point is always 0, resulting in a radius of infinity.