Prove that the ared of the large circle is equal to the sum of the area of the four small circles.

In the figure, semicircles are drawn with the sides of a triangles as diameters. Prove that the area of the largest semicircle is the sum of the areas of the smaller ones.

In the picture a triangle is formed by two mutually perpendicular tangents to a circle and a third tangent. Prove that the perimeter of the triangle is equal to the diameter of the circle.

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

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

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.

Using the given figure find the area of the shaded region (using formula to find the area of the circle)

In the figure, O is the centre of the large circle. Centre of the small circle is C. OP is a tangent to the small circle. angleBOQ=50^o . angleOAQ=......... . .

In the figure, O is the centre of the large circle. Centre of the small circle is C. OP is a tangent to the small circle. angleBOQ=50^o . angleOCP=....... . .

In the figure, O is the centre of the large circle. Centre of the small circle is C. OP is a tangent to the small circle. angleBOQ=50^o . angleAPO=....... . .