Inscribed Circle#554
A circle is called inscribed in a polygon if it is tangent to every side of the polygon.
Determine whether it is possible to inscribe a circle in a given convex polygon, and if so, find the coordinates of its center and its radius.
The first line contains the number of vertices (3 \leq n \leq 8). Each of the following lines contains two integers: the coordinates x_i and y_i of the vertices of the polygon, given in counterclockwise order. The values |x_i|,\ |y_i| \leq 1000.
If there exists a circle inscribed in the given polygon, print YES in the first line; otherwise, print NO. If the answer is yes, print in the second line the coordinates of the center of the circle and its radius. Output your answer with precision up to 10^{-6}.
Example 1
Example 2