If I have three points A, B, C and I know the distances between them and A is at 2D coordinates {0,0} and B is at {ab,0}, then what would be the formula to find the coordinates of the point C?
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The point
{cx, cy}
has to solve two equations:There are either two points which both have the desired distances. But based on
ac^2-cx^2
there may also be only one solution or none at all.You can use the distance formula (basically Pythagorean theorem) to find the distance between any two points on a coordinate plane.
http://www.purplemath.com/modules/distform.htm
If you don't place any further restrictions to the distances, your question is equivalent to "how to find the intersection of 2 circles":
http://mathworld.wolfram.com/Circle-CircleIntersection.html
Therefore, as Howard pointed out, there will be 0, 1, or 2 intersections points fulfilling the conditions you placed.