The resulting polygon must fir-in the circle. You only need to
determine circle radius and to check for possibility of the polygon
existance (extended triangle inequality).

To determine radiuse something like binary search is used. System of
equations is very simple and is solved that way.

Tip: be careful with the test when the center of circle is outside of
polygon.

P.S. Sorry for bad mathematical english...

> It's clear that the area is a convex polygon,and all its vertexs
share a comman circle.