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ZOJ Problem Set - 1199
Point of Intersection

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Given two circles on the same plane which are centered at (x1,y1) and (x2,y2) ,with radiuses r1 and r2, respectively.We can see that they have two common tangent lines in most of the cases.Now you are asked to write a programme to calculate the point of intersection of the two tangents if there exists one. ( See Figure 1 )

Figure. 1 Point of intersection


The input data consists of the information of several figures.The first line of the input contains the number of figures.
Each figure is described by two lines of data.Each line contains 3 integers constituting the coordinates of the center (x, y) and the radius r (>0) of a circle.


For each figure, you are supposed to output the coordinates (x, y) of the point of intersection if it exists.The x and y must be rounded to two decimal places and be separated by one space.If there is no such point exists simply output "Impossible."

Sample Input

0 0 10
0 0 5
0 0 10
10 0 1

Output for the Sample Input

11.11 0.00


The common tangent lines like the following figure don't take into account;

Source: Zhejiang University Local Contest 2002, Preliminary
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