Prove that in any parallelogram, the 'sum of the squares of all sides is equal to the sum of the squares of the diagonals'.

Prove that in any triangle, the outer angle at a vertex is equal to the sum of the inner arigles at the outer two vertices.

Find the three numbers in GP whose sum is 13 and the sum of whose squares is 91.

The sum of the perimeter of a circle and square is k , where k is a constant. Prove that the sum of their areas is least when the side of the square is double the radius of the circle.

Sum of the squares of the first n natural numbers exceeds their sum by 330 then find n.