solve the problem with complete steps asap.

Problem 8) (3 points): Let P be a polygon with exactly one hole. Sup- pose that P has n vertices including the hole vertices. Show that the number of triangles in any triangulation of P is n. Problem 9) (2 points): Draw a polygon that requires exactly 5 guards to cover it. Justify your answer. Problem 10) (3 points): The diameter of a point set S is the largest dis- tance between any two points of S. Show that the diameter of S is achieved by two vertices on the boundary of the convex hull of S