>>12811521Thats what im saying, D may lie on the circle but this is not necessarily the case, so the problem as posed cannot be solved in general.
The circle we seek has form x^2+y^2=r^2. We have three unknowns to solve for.
We draw circles around each point with equal radius, and seek a radius such that all three circles converge at one point (the center of the circle we seek). This gives us the set of equations:
Ax^2 +Ay^2 = r^2
Bx^2 + By^2 = r^2
Cx^2 + Cy^2 = r^2
Note: a circle is a set of equidistant points, so these three must be equidistant from the center, so Ar=Br=Cr=r.
Adding another point adds another equation to our set, and overconstrains our system. Therefore a general solution to a circle passing through four points does not exist. qed
