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The triangle ABC was divided into three triangles ABO, BCO, ACO. From the center of a circle O draw to each side of the triangle ABC radius r. P_{ABC} = P_{ABO} + P_{BCO} + P_{ACO}; P_{ABC} = 1/2 * a * r + 1/2 * b * r + 1/2 * c * r, 2P_{ABC} = a * r + b * r + c * r; 2P_ABC = r * (a+b+c) /: (a+b+c); 2P_{ABC} / a+b+c = r; r = 2P_{ABC} / a+b+c.