UVa 10451 - Ancient Village Sports

10451 - Ancient Village Sports
http://acm.uva.es/p/v104/10451.html

Summary
You are given the Area of the polygon. You'll have to find

area for spectators = area of the outer circle - area of the polygon

area for officials = area of the polygon - area of the inner circle

remember PI = 2 * acos(0)

and your output should be rounded currect to 5 decimal points

Explanation
find the area of the small triangle made up the polygon [if you have solved 10432 then you can get the formula from there] from there you can find the area of the outer circle

and you can find the area of the inner circle through this formula

area of the inner circle = Area of the polygon / (number of sides * tan(pi/number of sides))

Sample Input
3 0.43301 6 2.59808 9 6.18182 0 2.33333

Sample Output
Case 1: 0.61418 0.17121 Case 2: 0.54352 0.24188 Case 3: 0.53226 0.25314