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

Prove that the sum of the squares of the diagonals of rhombus is equal to the sum of the squares of the sides.

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals

The circles which are not congruent touch externally. The sum of their areas is 130picm^(2) and distance between their centres is 14 cm . Find the radii of the two circles.

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

Prove that in a right triangle, the square of the hypotenure is equal to the sum of the squares of the others two sides.

Prove that among all the rectangles of the given perimeter, the square has the maximum area.

Prove that among all the rectangles of the given area, square has the least perimeter.

A point moves such that the sum of the squares of its distances from the two sides of length ‘a’ of a rectangle is twice the sum of the squares of its distances from the other two sides of length b. The locus of the point can be:

If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum of the squares of these terms is