CBSE Class 10 Mathematics Circles Worksheet Set G

Read and download free pdf of CBSE Class 10 Mathematics Circles Worksheet Set G. Students and teachers of Class 10 Mathematics can get free printable Worksheets for Class 10 Mathematics Chapter 10 Circles in PDF format prepared as per the latest syllabus and examination pattern in your schools. Class 10 students should practice questions and answers given here for Mathematics in Class 10 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 10 Mathematics Worksheets prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems with solutions on daily basis to get more score in school exams and tests

Worksheet for Class 10 Mathematics Chapter 10 Circles

Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 10 Circles in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks

Class 10 Mathematics Worksheet for Chapter 10 Circles

 

CIRCLES

Q.- If radii of two concentric circles are 4 cm and 5 cm, then the length of the chord of one circle which is tangent to the other circle is: 

WT_circles test 23

a. 9 cm

b. 3 cm

c. 1 cm

d. 6 cm

Ans- d. 6 cm
Explanation: Here OC is perpendicular to AB.
Then OC bisects AB i.e., AC = BC
Now, in triangle OAC,OA2=AC2+OC2
(5)2 = AC2 + (4)2 AC2 = 25 - 16
AC = 3 Therefore, length of tangent AB = AC + BC = 3 + 3 = 6 cm
 
Q.- A circle is inscribed inΔABC having sides 8 cm, 10 cm and 12 cm as shown in the figure. Then the measure of AD and BE are... 
WT_circles test 24
a. AD = 8 cm, BE = 5 cm.
b. AD = 8 cm, BE = 6 cm
c. AD = 5 cm, BE = 7 cm
d. AD = 7 cm, BE = 5 cm
 
Ans- d. AD = 7 cm, BE = 5 cm
Explanation: Let AD = and BE = y
∴ BD = 12 - x BE = y
But BD = BE (Tangents to a circle from an external point B)
=> y = 12 - x
=> x + y = 12 ……….(i)
Also, AF = x
and CF = 10 - x
and CE = 8 - y
∴ 10 - x = 8 - y
x - y = 2……..(ii)
On solving eq. (i) and (ii), we get
x = 7 and y = 5
Therefore AD = 7 cm and BE = 5 cm
 
Q.- At which point a tangent is perpendicular to the radius? 
 
Ans- A line which intersects a circle at any one point is called the tangent. The tangent at any point of a circle is perpendicular to the radius through the all point of contact.

14. Prove that parallelogram circumscribing a circle is a rhombus. 

Ans-

WT_circles test 25 

Given ABCD is a parallelogram in which all the sides touch a given circle
To prove:- ABCD is a rhombus
Proof:-
∴ ABCD is a parallelogram
∴ AB = DC and AD = BC
Again AP, AQ are tangents to the circle from the point A
∴ AP = AQ
Similarly, BR = BQ
CR = CS
DP = DS
∴ (AP + DP) + (BR + CR) = AQ + DS + BQ + CS = (AQ + BQ) + (CS + DS)
=> AD + BC = AB + DC
=>BC + BC = AB + AB [ AB = DC, AD = BC]
=>2BC = 2AB
=>BC = AB
Hence, parallelogram ABCD is a rhombus
 
Q.- A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC. 
 
Ans-
 
WT_circles test 26
∴AP, AS are tangents from a point A (Outside the circle) to the circle.
∴ AP = AS
Similarly BP = BQ
CQ = CR
DR = DS
Now AB + CD = AP + PB + CR + RD
= AS + BQ + CQ +DS
= (AS +DS) + (BQ + CQ)
= AD + BC
AB + CD = AD + BC
 
Q.- In given Fig. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA + AR = XB + BR. 
WT_circles test 27
 
Ans- Since the lengths of tangents from an exterior point to a circle are equal.
XP = XQ ..........(i)
AP = AR ........ (ii)
BQ = BR ......... (iii)
Now Xp = XQ i.e. XA + AP = XB + BQ
XA + AR = XB + bR
Hence proved.
 
Q.- In the given figure, find the perimeter of ABC, if AP = 10 cm. 

WT_circles test 28

Ans- BC touches the circle at R
Tangents drawn from external point to the circle are equal.
AP = AQ, BR = BP
And CR = CQ
Perimeter of ΔABC = AB + BC + AC
= AB + (BR + RC) + AC
= AB + BP + CQ + AC
= AP + AQ = 2AP = 2 ×10 = 20 cm

 

AREAS RELATED TO CIRCLES

 

KEY POINTS

1. Circle: The set of points which are at a constant distance from a fixed point in a plane is called a circle.R

2. Circumference: The perimeter of a circle is called its circumference.

3. Secant: A line which intersects a circle at two points is called secant of the circle.

4. Arc: A continuous piece of circle is called an arc of the circle.

5. Central angle: - An angle subtended by an arc at the center of a circle is called its central angle.

6. Semi-Circle: - A diameter divides a circle into two equal arcs. Each of these two arcs is called a semi-circle.

7. Segment: - A segment of a circle is the region bounded by an arc and a chord, of a circle.

8. Sector of a circle: The region enclosed by an arc of a circle and its two bounding radii is called a sector of the circle.

9. Quadrant: - One fourth of a circle/ circular disc is called a quadrant. The central angle of a quadrant is 900.

LEVEL-I

1. If the perimeter of a circle is equal to that of square, then the ratio of their areas is

i. 22/7

ii. 14/11

iii. 7/22

iv. 11/14

2. The area of the square that can be inscribed in a circle of 8 cm is

i. 256 cm2

ii. 128cm2

iii. 64√2cm2

iv. 64cm2

3. Area of a sector to circle of radius 36 cm is 54 cm2 . Find the length arc of the corresponding arc of the circle is

i. 6

ii. 3

iii. 5

iv. 8

4. A wheel has diameter 84 cm. The number of complete revolution it will take to cover 792 m is.

i. 100

ii. 150

iii. 200

iv. 300

5. The length of an arc of a circle with radius 12cm is 10 cm. The central angle of this arc is.

i. 1200

ii. 60

iii. 750

iv. 1500

6. The area of a circle whose circumference π cm is

i. 11/2 cm2

ii. π/4 cm2

iii. π/2 cm2

iv. None of these

7. In figure ‘o’ is the centre of a circle. The area of sector OAPB is 5/18 of the area of the circle find x.

8. If the diameter of a semicircular protractor is 14 cm, then find its perimeter.

9. The diameter of a cycle wheel is 21cm. How many revolutions will it make to travel 1.98km?

10. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

LEVEL – II

1. Find the area of the shaded region in the figure if AC=24 cm ,BC=10 cm and o is the center of the circle (use A B C

2. The inner circumference of a circular track is 440m. The track is 14m wide. Find the diameter of the outer circle of the track. [Take=22/7]

 

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CBSE Class 10 Mathematics Chapter 10 Circles Worksheet

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