 Hello and welcome to the session. In this session, first we will discuss about the circumference of a circle. We know that the distance covered by travelling once round a circle is called its perimeter or you can also say is called its circumference. So the formula for the circumference of a circle is given by 2 pi r where r is the radius of the circle and pi is a constant with value 22 upon 7 or 3.14 approximately. Consider this circle with radius r given as 14 centimeters. So now circumference of the circle is given as 2 pi r. So this is the circumference of the circle when we are given the radius r of the circle. Now we shall discuss about the area of a circle. Area is basically the region enclosed by a closed figure. If we are given the circle with centre O then the region enclosed by this circle that is this shaded region would be the area of the circle. Formula for the area of circle is given by pi r square where this r is the radius of the circle and pi is a constant with value 22 upon 7 or 3.14 approximately. Consider this circle with radius r given as 14 centimeters. We are supposed to find the area of the circle. This would be given by pi r square. So this is the area of the circle when we are given the radius r of the circle. Next we will find out the length of an arc of a sector of a circle. Portion of the circular region enclosed by 2 radii and the corresponding arc that is this shaded region is called the sector of the circle. So the region OAPB is the sector of the circle. Even this unshaded region is also the sector of the circle. This is called the major sector and this is the minor sector. If the angle AOB is given to be of major theta this is called the angle of the sector. Now the angle of the major sector would be given by 360 degrees minus the angle of the minor sector that is theta. So now the formula for the length of an arc is given by theta that is the angle of the sector upon 360 multiplied by the circumference of the circle that is 2 pi r where r is the radius of the circle and theta is the angle of sector. Consider a circle with radius r given as 14 centimeters and the angle of sector theta at 60 degrees we are supposed to find the length of the arc AB. Thus we have length of the arc AB is given by the formula theta that is 60 upon 360 multiplied by 2 pi r. So this is the length of the arc AB when we are given the radius and the angle of sector theta. Now we discuss the area of sector of a circle. This is the sector of the circle with angle of sector as theta. We are supposed to find the area of the sector which is given by the formula theta that is the angle of sector upon 360 multiplied by the area of the circle that is pi r square. If we are supposed to find the area of this major sector that is this area then the angle of sector would be taken as that is this angle would be taken as 360 degrees minus the angle of the minor sector that is theta. Consider a circle of radius r given as 14 centimeters and the angle of sector that is theta is given to be of measure 60 degrees we are supposed to find the area of the sector OAPB. So we have area of the sector OAPB is given by the formula theta that is 60 upon 360 multiplied by pi r square. So this is the area of the sector OAPB when we are given the radius and the angle of the sector. Next is the area of segment of a circle. Portion of the circular region enclosed between a chord and the corresponding arc that is this region this shaded region is called the segment of the circle. This unshaded region is the major segment and this shaded region is the minor segment in general the area of segment of a circle is given by the area of corresponding sector that is if we need to find the area of major segment then we will consider area of major sector here and if we need to find the area of minor segment then we will consider the area of minor sector here. This minus area of the corresponding triangle that is area of this minor segment would be equal to the area of this minor sector that is OAPB minus the area of the triangle OAB. An area of the major segment that is this region is equal to the area of the circle minus the area of the minor segment. Consider a circle of radius r given as 14 centimeters and the angle of sector theta is given as 60 degrees we are supposed to find the area of the segment APB. So we have area of segment APB is given by area of sector OAPB minus area of triangle OAB. We already have found out the area of sector OAPB in the previous section which is equal to this minus area of triangle OAB is given by this. So this is the area of the segment APB when we are given the radius r of the circle and the angle of sector theta. This completes the session hope you have understood how do we find out the perimeter and area of a circle length of an arc of a sector of a circle area of the sector and area of the segment.