Triangulating non-self-intersecting 2D Polygons

a) Provide an algorithm to test if a polygon P1,P2,,..,Pn with vertices in counter-clockwise order is convex?

b) Provide an algorithm to triangulate a convex polygon. The algorithm outputs n-2 triangles (such as P1,P2,P3 , P2,P4,P7 etc.) What is its time complexity of the algorithm?

c) Will the algorithm above work on concave polygons. If yes, prove it; If not, provide a counterexample and provide an algorithm that will work on concave polygons. What is the complexity of this algorithm?