{"trustable":false,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\r\n\tYou\u0026#39;re fighting against a monster. You have a special weapon that can shoot a laser beam. The laser beam can be seen as a cylinder along the z-axis, So when look from above the XY plane, the laser beam is actually a circle centered at (0,0) (yes, you cannot change the position of center). The monster is a convex polygon (well, you may think of it as a very thin prism) with n vertices surrounding the origin (i.e. (0,0) is strictly inside the monster, not on his boundary).\u003c/p\u003e\r\n\u003cp\u003e\r\n\tYou know that, when the common area of the laser beam and the monster is at least R, the monster dies. Since larger laser beam consumes more power, you\u0026#39;re interested in the minimum radius of the laser beam.\u003c/p\u003e\r\n\u003cp\u003e\r\n\tWrite a program to find the minimum radius. It is guaranteed that (0 \u0026pound;\u003cem\u003eR\u003c/em\u003e \u0026pound;\u003cem\u003eA\u003c/em\u003e), where \u003cem\u003eA\u003c/em\u003e is the area of the monster.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003e\r\n\tThe input consists at most 10cases. Each case starts with a single integer \u003cem\u003en \u003c/em\u003e(3 \u0026pound;\u003cem\u003en\u003c/em\u003e\u003cem\u003e \u003c/em\u003e\u0026pound;50) and a floating-point number R followed by \u003cem\u003en\u003c/em\u003e lines of two real numbers: the coordinates of the monster. The points are arranged in counter-clockwise order or clockwise order. The last test case is followed by a single zero, which should not be processed. The meaning of N and R are given in the problem statement.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003e\r\n\tFor each test case, print the case number and the minimum radius, to 2 decimal places. Inputs will be such that small precision errors will not change the visible output if you use double-precision floating-point numbers.\u003c/p\u003e"}},{"title":"Sample Input","value":{"format":"HTML","content":"\u003cp\u003e\r\n\t3 1.60\u003cbr /\u003e\r\n\t-1 -1\u003cbr /\u003e\r\n\t1 -1\u003cbr /\u003e\r\n\t0 1\u003cbr /\u003e\r\n\t0\u003c/p\u003e"}},{"title":"Sample Output","value":{"format":"HTML","content":"\u003cp\u003e\r\n\tCase 1: 0.93\u003c/p\u003e"}}]}