The picture below shows two circles, each passing through the center of the other. Calculate the area of the region common to both.

The pictures below show circles through the vertices of a square and a rectangle.Calculate the areas of the circles

The figure shows three circles drawn with their centers on each vertex of an equilateral triangle' and passing through the other two vertices. Find the area of the region common to all three.

Two identical concentric rings each of mass M and radius R are placed perpendicular to each other. What is the moment of inertia about an axis passing through the center of this system and perpendicular to the plane of one of the rings?

The picture shows two circles with the same centre and two triangles formed by joining the centre to the points of intersection of the circles with two radii of the larger circle. prove that these triangles are similar .

The picture on the right shows two circles centred on the same point and a line intersecting them.Prove that the parts of the line between the circles on either side are equal.

The bottom side of the quadrilateral in the picture is a diameter of the circle and the top side is ạ chord parallel to it. Calculate the area of the quadrilateral.

In the picture, the tangent to the circumcircle of a regular pentagon through a vertex is shown. Calculate the angle which the tangent makes with the two sides of the pentagon through the point of contact.

The picture shows a triangle formed by three tangents to a circle. . Calculate the length of each tangent from the corner of the triangle to the point of contact.

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.