Consider a convex polygon.
a. (i) Derive a general formula for the number of diagonals that can be drawn in a convex polygon of n sides.
b. (ii) A convex polygon has 20 sides. Calculate the total number of its diagonals.
c. (iii) All the diagonals of the 20-gon obtained in part (ii) are drawn. One vertex, together with all segments incident to that vertex, is then removed. Determine the number of diagonals that still remain inside the figure.