126 - The 10th Zhejiang Provincial Collegiate Programming Contest - E
Marjar wants to play egg-painting. It needs to peel off some part of the egg shell and take out the yolk, and then paint a picture on the egg shell. But Marjar don't want to destroy the yolk. This seems quite difficult for him to take the yolk out. He decides to make a hole that is a spherical polygon consisting of n arcs of the great circles connecting n vertices. But he didn't know whether the yolk could come out or not from the hole he created on the egg shell. Your task is helping him to determine whether the hole is big enough. His egg is a sphere with radius R while the yolk is also a sphere with radius r inside the egg.
There are multiple test cases. The first line of input contains an integer T (0 < T ≤ 50) indicating the number of test cases. Then T test cases follow.
The first line of each test case contains 3 integers n, R and r(0 < n ≤ 50, 0 < r ≤ R ≤ 10000). Then n lines follow, telling the vertices of the hole in counterclockwise order when viewing from outside the egg. Each of the n lines contains 2 real numbers, each of which contains at most 2 digits after the decimal point, indicating the longitude and the latitude of the vertex. The longitude and the latitude are measured in degree. The longitude will be in (180, 180] while the latitude will be in [-90, 90]. It is guaranteed that the spherical polygon will not cross itself.
For each test case, output "Yes" if it is possible to take out the yolk from through the hole in one line. Otherwise output "No".
1 3 10 1 0 0 90 0 0 90