Three non-collinear points do not determine a unique spherical triangle.
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Any plane figure with more than three sides. Any spherical triangle.
To determine if two sets of points are collinear, you can calculate the slopes of the lines formed by connecting the points in each set. If the slopes are equal, then the points are collinear. Another method is to calculate the area of the triangle formed by the three points in each set. If the area is zero, then the points are collinear. Lastly, you can use the determinant of a matrix method to check if the points lie on the same line.
A spherical surface, with its center at the given point, and its radius equal to the given distance.
Square the two smaller ones and see if that total equals the square of the larger one.