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Drawing a triangle in a coordinate plane given its three sides

The length of three sides of the triangle, a, b and c will be given, and I need to find the coordinates of the vertices. The center (probably the circumcenter) can either be the origin or (x,y).

Can anyone point me in the right direction?

Solution

  • I've read brainjam's answer and checked whether his answer is true and he is right. Calculation: O(0;0), A(a;0) and B(x;y) are the three points of the triangle. C1 is the circle around A and r1 = c; C2 is the circle around O and r2 = b. B(X;Y) is the intersection of C1 and C2, which means that the point is on both of the circles.

    alt text

    C1: (x - a) * (x - a) + y * y = c * c

    C2: x * x + y * y = b * b

    y * y = b * b - x * x

    (x - a) * (x - a) + b * b - x * x = c * c

    x * x - 2 * a * x + a * a + b * b - x * x - c * c = 0

    2 * a * x = (a * a + b * b - c * c)

    x = (a * a + b * b - c * c) / (2 * a)

    y * y = b * b - ((a * a + b * b - c * c) / (2 * a)) * ((a * a + b * b - c * c) / (2 * a))

    y = +- sqrt(b * b - ((a * a + b * b - c * c) / (2 * a)) * ((a * a + b * b - c * c) / (2 * a)))