areas related to circles - class 10 maths
TRANSCRIPT
CIRCLESMade by :- Amit choube
Class :- 10th ‘ B ’
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 .
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 .
Circle – DefinitionThe collection of all the points in a plane which are at a fixed distance from in the plane is called a circle . orA 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.
1. Radius – The 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
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 .
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 .
1. 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
Segment – the region between a chord and either of its arc is called a segment of the circle .
Major segment
Minor segment
Here , in the given fig. We can clearly see major and minor segment .
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 .
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)
Area of a circleArea 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.
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 =
Area of a sector .
Following are some important points to remember 1. A minor sector has an angle , (say) , subtended at
the centre of the circle , whereas a major sector has no angle .
2. The sum of arcs of major and minor sectors of a circle is equal to the circumference of the circle .
3. The sum of the areas of major and minor sectors of a circle is equal to the areas of the circle .
4. The boundary of a sector consists of an arc of the circle and the two radii .
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.
Area of a sector.
Some useful results to remember .1. 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 .
2. 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 . ͦ
Area of a segment of a circle
Thank you