 Hi and welcome to the session. Today we will learn about circles. Here we have a circle with center O. Now let's see what is the radius and diameter of the circle. This stands from the center to any point on the circle that is the boundary of the circle is the radius of the circle and is denoted by R. Now diameter is twice of radius. So this is the diameter of the circle that is the length of the line segment joining two points on the boundary of the circle and passing through the center and we denoted by D. Now let's see what is the circumference of a circle. Circumference of a circle is the distance around a circular region or we can say that the perimeter of the circle is called its circumference. So here in this circle if we start from the point A and we move along the boundary of the circle and then we come back at the point A then the distance covered is the circumference of this circle. Circumference of the circle is denoted by C. Now let's see the relationship between the circumference and the diameter of the circle. The ratio of the circumference to the diameter that is C upon D is a constant that is pi whose approximate value is equal to 222 by 7 or 3.14. Thus we can find out the circumference of the circle using the formula circumference is equal to 2 pi R that is 2 into pi into radius of the circle. Let's take an example for this. Suppose we are given that the circumference of the circle is 26.4 centimeters and we need to find the diameter of the circle. Now we know that circumference of the circle is given by 2 pi R. Now we are given the value of circumference as 26.4 centimeters. So let us substitute the values. We have 26.4 centimeters is equal to 2 into 22 by 7 that is pi into R. So from this we get radius R is equal to 26.4 into 7 upon 2 into 22 centimeters which will be equal to 4.2 centimeters. Now we need to find the value of diameter and diameter is equal to 2 into R. So this will be equal to 2 into 4.2 centimeters that is 8.4 centimeters. Now let's move on to area of a circle. Area of a circle is given by pi R square. We will take an example for this also. We are given that a circular flat bed is surrounded by a path 4 meter wide. This is the path so that means its width is 4 meters. The diameter of the flat bed is 66 meters and we need to find the area of this path. Now to find area of the path what we will do is we will subtract the area of the inner circle from the area of the outer circle. Then we will get the area of this path. So we have area of path is equal to area of outer circle minus area of inner circle. Now for inner circle we are given that the diameter is equal to 66 meters that means radius will be equal to 66 upon 2 meters that is 33 meters. So area of inner circle will be equal to pi R square that is pi into 33 square meters square. Now radius of the inner circle is 33 meters and width of the path is 4 meters. So radius of the outer circle will be radius of inner circle plus width of the path that means for outer circle radius R will be equal to radius of the inner circle plus width of the path this will be equal to 33 meters plus 4 meters which is equal to 37 meters. Now let's find out the area of outer circle this will be equal to pi R square which is equal to pi into 37 square meters square. Thus area of the path will be equal to area of outer circle that is pi into 37 square meters square minus area of inner circle pi into 33 square meters square. Which will be equal to 3.14 into 37 square minus 3.14 into 33 square meters square as the value of pi is 3.14 and on simplifying this gives 879.20 meters square approximately. So area of the path is equal to 879.20 meters square. Thus in this session we have learnt about perimeter and area of a circle. With this we finished this session hope you must have enjoyed it. Goodbye take care and keep smiling.