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Language: Point of view in Flatland
Description Everything is flat in Flatland. The planets are round but they are flat, that is, they are discs in a plane. The centers of three planets in Flatland are given and their radii. Find the point in Flatland from which all three planets are visible at the same angle, that is, they appear to have the same size measured as angular diameter. Let's call such a point an Input Input consists of several cases, each case is presented at a single line. Each line has nine numbers, three for each disc. Each triple has Output For each case of input, print the Sample Input 10 10 1 30 30 1 50 10 1 0 30 1.0 30 0 1.0 40 40 1.0 10 30 1.0 31 0 1.0 42 43 1.0 10 42 1 62.8 62.8 1 52.5 -25.3 1 10 42 1.1 62.8 62.8 1.2 52.5 25.3 25 0 0 0 0 0 0 0 0 0 Sample Output 30.00 10.00 23.00 23.00 31.58 22.76 49.27 19.73 No solution Hint To simplify the problem you may assume that: - The discs centers are not all collinear.
- The discs are totally disjoint.
- The discs are transparent and non-refractive. That is, a disc is visible and has the same apparent shape and size, whether or not there's another disc in front of it.
- The input data are such that the existence or non-existence of such a point is computable, even with slight rounding error. But use double-precision, eh?
Source Waterloo Local Contest, 2006.5.27 |

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