Line belt

In a two-dimensional plane there are two line belts, there are two segments AB and CD, lxhgww's speed on AB is P and on CD is Q, he can move with the speed R on other area on the plane.
How long must he take to travel from A to D?

在二维平面中有两条线段AB和CD，lxhgww的速度在AB上是P，在CD上是Q，他可以在平面上的其他区域以速度R移动。
从A到D旅行最少需要多长时间？

其中一种情况的示意图如下

The first line is the case number T.
For each case, there are three lines.
The first line, four integers, the coordinates of A and B: Ax Ay Bx By.
The second line , four integers, the coordinates of C and D:Cx Cy Dx Dy.
The third line, three integers, P Q R.
0<= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy<=1000
1<=P，Q，R<=10

第一行是案例编号T.
对于每种情况，有三行。
第一行，四个整数，A和B的坐标：Ax Ay Bx By。
第二行，四个整数，C和D的坐标：Cx Cy Dx Dy。
第三行，三个整数，P Q R
0 <= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy <= 1000
1 <= P，Q，R <= 10

The minimum time to travel from A to D, round to two decimals.

从A运动到D的最短时间，四舍五入到两位小数。（貌似若结果与标准答案误差在0.01以内，是可以AC的）

8
0 0 4 1
4 1 0 2
8 8 1
0 0 0 100
100 0 100 100
2 2 1
8 0 23 8
4 2 91 0
4 9 10
0 0 2 2
0 2 2 0
4 3 1
1 8 1000 10
0 689 10 1000
90 1 20
4 9 4 20
4 41 4 60
4 4 1
4 9 4 20
4 91 4 60
4 3 1
0 5 8 5
2 5 4 0
6 9 3

1.03
136.60
8.30
0.83
49.60
28.50
42.75
0.93