Areas related to Circles - class 10 maths

This a ppt which is based on chapter circles of class 10 maths it is a very good ppt which will definitely enhance your knowledge . it will also clear all concepts and doubts about this chapter and its topics

1. CIRCLES Made by :- Amit choube Class :- 10 th ‘ B ’

2. Introduction In this power point presentation we will discuss about Circle and its related terms . Concepts of perimeter and area of a circle . Finding the areas of two special parts of a circular region known as sector and segment . Finding the areas of some combinations of plane figures involving circles or their parts .

3. Contents Circle and its related terms . Area of a circle . Areas related to circle . Perimeter of a circle . Sector of a circle and its area . Segment of a circle and its area Areas of combinations of plane figures .

4. Circle – Definition The collection of all the points in a plane which are at a fixed distance from in the plane is called a circle . or A circle is a locus of a point which moves in a plane in such a way that its distance from a fixed point always remains same.

5. Radius – T he line segment joining the centre and any point on the circle is called a radius of the circle . O P Here , in fig. OP is radius of the circle with centre ‘O’ . Related terms of circle

6. 2 . A circle divides the plane on which it lies into three parts . They are The Interior of the circle . The circle . Exterior The exterior of the circle . Interior circle Here , in the given fig . We can see that a circle divides the plane on which it lies into three parts .

7. 3. Chord – if you take two points P and Q on a circle , then the line segment PQ is called a chord of the circle . 4. Diameter – the chord which passes through the centre of the circle is called a diameter of the circle . O P R Here in the given fig. OR is the diameter of the circle and PR is the chord of the circle . Note :- A diameter of a circle is the longest chord of the circle .

8. Arc – the piece of circle between two points is called an arc of the circle . Q . Major Arc PQR P . . R Minor Arc PR Here in the given fig. PQR is the major arc because it is the longer one whereas PR is the minor arc of the given circle . When P and Q are ends of a diameter , then both arcs are equal and each is called a semicircle

9. Segment – the region between a chord and either of its arc is called a segment of the circle . M ajor segment Minor segment Here , in the given fig. We can clearly see major and minor segment .

10. Sector – the region between two radii , joining the centre to the end points of the arc is called a sector . A B Here in the given fig. you find that minor arc corresponds to minor sector and major arc correspondence to major sector .

11. Perimeter of a circle The distanced covered by travelling around a circle is its perimeter , usually called its circumference . We know that circumference of a circle bears a constant ratio with its diameter . (diameter = 2r)  

12. Area of a circle Area of a circle is , where is the radius of the circle . We have verified it in class 7 , by cutting a circle into a number of sectors and rearranging them as shown in fig.  

13. Area and circumference of semicircle Area of circle = Area of semi – circle = (Area of circle) Area of semicircle and Perimeter of circle = Perimeter of semi circle = Perimeter of semi circle =  

14. Area of a sector . Following are some important points to remember A minor sector has an angle , (say) , subtended at the centre of the circle , whereas a major sector has no angle . The sum of arcs of major and minor sectors of a circle is equal to the circumference of the circle . The sum of the areas of major and minor sectors of a circle is equal to the areas of the circle . The boundary of a sector consists of an arc of the circle and the two radii .  

15. If an arc subtends an angle of 180 at the centre , then its arc length is . If the arc subtends an angle of θ at the centre , then its arc length is If the arc subtends an angle θ , then the area of the corresponding sector is Thus the area A of a sector of angle θ then area of the corresponding sector is Now,   Area of a sector.

16. Area of a sector.

17. Some useful results to remember . Angle described by one minute hand in 60 minute =360 ͦ Angle described by minute hand in one minute = Thus , minute hand rotates through an angle of 6 in one minute . Angle described by hour hand in 12 hours = 360 ͦ Angle described hour hand in one minute = Thus , hour hand rotates through 30 ͦ in one minute .  

18. Area of a segment of a circle

19. Thank you