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    Nine-point Circle

    Result

    circle | radius (a b c)/(2 sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))) = (0.5 a b c)/sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) (assuming edge lengths a, b, c)

    Visual representation

    Visual representation

    Equation

    (x - x_0)^2 + (y - y_0)^2 = (a^2 b^2 c^2)/(4 (a + b - c) (a - b + c) (-a + b + c) (a + b + c)) (assuming edge lengths a, b, c)

    Properties of nine point circle

    center | (x_0, y_0) diameter | (a b c)/sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) area enclosed | (π a^2 b^2 c^2)/(4 (a + b - c) (a - b + c) (-a + b + c) (a + b + c))≈(0.785398 a^2 b^2 c^2)/((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) circumference | (π a b c)/sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c))≈(3.14159 a b c)/sqrt((a + b - c) (a - b + c) (-a + b + c) (a + b + c)) (assuming edge lengths a, b, c)

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