Problem G
Zipline

A zipline is a very fun and fast method of travel. It uses a very strong steel cable, connected to two poles. A rider (which could be a person or some cargo) attaches to a pulley which travels on the cable. Starting from a high point on the cable, gravity pulls the rider along the cable.
Your friend has started a company which designs and installs ziplines, both for fun and for utility. However, there’s one key problem: determining how long the cable should be between the two connection points. The cable must be long enough to reach between the two poles, but short enough that the rider is guaranteed to stay a safe distance above the ground. Help your friend determine these bounds on the length.
The cable connects to two vertical poles that are
![\includegraphics[width=0.7\textwidth ]{zipline.png}](/problems/zipline/file/statement/en/img-0002.png)
Input
The input starts with a line containing an integer
Output
For each zipline, print a line of output with two lengths
(in meters): the minimum and maximum length the cable can be
while obeying the above constraints. Both lengths should have
an absolute error of at most
Sample Input 1 | Sample Output 1 |
---|---|
2 1000 100 100 20 100 20 30 2 |
1000.00000000 1012.71911209 100.49875621 110.07270325 |