{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"Your team is to write a program that, given the Cartesian coordinates of three points on a plane, will find the equation of the circle through them all. The three points will not be on a straight line. \r\u003cbr\u003eThe solution is to be printed as an equation of the form \r\u003cbr\u003e\u003cpre\u003e\t(x - h)^2 + (y - k)^2 \u003d r^2\t\t\t\t(1)\u003c/pre\u003e\r\u003cbr\u003eand an equation of the form \r\u003cbr\u003e\u003cpre\u003e\tx^2 + y^2 + cx + dy - e \u003d 0\t\t\t\t(2)\u003c/pre\u003e\r\u003cbr\u003e"}},{"title":"Input","value":{"format":"HTML","content":"Each line of input to your program will contain the x and y coordinates of three points, in the order Ax, Ay, Bx, By, Cx, Cy. These coordinates will be real numbers separated from each other by one or more spaces."}},{"title":"Output","value":{"format":"HTML","content":"Your program must print the required equations on two lines using the format given in the sample below. Your computed values for h, k, r, c, d, and e in Equations 1 and 2 above are to be printed with three digits after the decimal point. Plus and minus signs in the equations should be changed as needed to avoid multiple signs before a number. Plus, minus, and equal signs must be separated from the adjacent characters by a single space on each side. No other spaces are to appear in the equations. Print a single blank line after each equation pair."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e7.0 -5.0 -1.0 1.0 0.0 -6.0\r\n1.0 7.0 8.0 6.0 7.0 -2.0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e(x - 3.000)^2 + (y + 2.000)^2 \u003d 5.000^2\r\nx^2 + y^2 - 6.000x + 4.000y - 12.000 \u003d 0\r\n\r\n(x - 3.921)^2 + (y - 2.447)^2 \u003d 5.409^2\r\nx^2 + y^2 - 7.842x - 4.895y - 7.895 \u003d 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}