一个ACm/ICPC问题

给你一个三角形的三边，一个圆的半径。两个图形放在平面上，可以移动，求最大公共面积！
期待高手
Problem C: Circle and Triangle
Time Limit: 1 sec
Description
LMY and YY are geometry lovers. They enjoy challenging each other with interesting geometry problems. One day, LMY puts a circle and a triangle on a plane. Then YY moves them. They find that the overlapping area of the circle and the triangle varies as the relative position between the two changes. LMY and YY want to find out the largest common area.
The Input
Input consists of one or more lines. For each line, there are four integers describing one test case: the lengths of three sides of a triangle a, b, c; and the radius of a circle r; where 1≤a≤b≤c≤100, 1≤r≤100, and a+b>c.End of input is indicated by a line consisting four zeros.
The Output
For each test case, output a single line showing the largest overlapping area of the circle and the triangle. The precision should be 10-2.
Sample Input
3 4 5 1 （分别为三角形 三边 和半径）
5 5 8 4
0 0 0 0

Sample Output
3.14
12.00