1) Prove that a (convex or concave) polygon having the perimeter of 2 can be placed inside a circle which has the diameter of 1 pefectly
Hint from teacher:using symmetry of point.
2) With each point X inside convex polygon:A(1)A(2)...A(2009),we set S(X)=XA(1)+XA(2)+...+XA(2009)
Do 2 point P,Q exist inside the polygon that they satisfy:
PQ=1 and |S(P)-S(Q)|=2007