CBSE Class 10 Mathematics Circles Worksheet Set E

Read and download free pdf of CBSE Class 10 Mathematics Circles Worksheet Set E. 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

 

CIRCLE

Q.- In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110o, then find ∠ PTQ. 
WT_circles test 16

 

Ans- ∠POQ = 110o
∠OPT = 90o [Angle between tangent and radius through the point of contact]
∠OQT = 90o [Angle between tangent and radius through the point of contact]
In quadrilateral OPTQ,
∠POQ + OQT + PTQ = 360o
∴The sum of all the angles of a quadrilateral is 360o.
=> 110o + 90o + 90o + PTQ = 360o
=> 290o + PTQ = 360o
=> PTQ = 360o - 290o = 70o
=> Hence, the PTQ is 70o.
 
Q.- From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D respectively.If PA = 14 cm, find the perimeter of ΔPCD. 
 
Ans- We have,
WT_circles test 17
AC = CE, BD = DE
And, AP = BP = 14 cm
∴ Perimeter of ΔPCD = PC + CD+ PD
=>Perimeter of ΔPCD = PC + (CE + ED) + PD
= (PC + CE) + (ED + PD)
= (PC + AC) + (BD + PD)
= PA + PB
= 14 + 14
= 28
∴ Perimeter of ΔPCD = 28 cm.
 
Q.- The tangent at a point C of a circle and a diameter AB when extended intersect at P. If
∠PCA = 110o, find ∠CBA.
[Hint: Join C with centre O]. 

WT_circles test 19

Ans-According to the question,we are given that tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA = 110o, find ∠CBA.
WT_circles test 18
OC and CP are radius and tangent respectively at contact point C.
So, ∠OCP = 90o
∠OCA = ∠ACP -∠ OCP
=> ∠OCA = 110o - 90o
=> ∠OCA = 20o
 
In ΔOAC,
OA = OC [Radii of same circle]
Therefore, ∠OCA = ∠A = 20o [Since, Angles opposite to equal sides are equal]
CP and CB are tangent and chord of a circle.
Therefore, ∠CBP = ∠A [Angles in alternate segments are equal]
In ΔCAP,
∠P + ∠A + ∠ACP = 180o [Angled sum property of a triangle]
=> ∠P + 20o + 110o = 180o
=> ∠P = 180o - 130o
=> ∠P = 50o
In Δ BPC,
Exterior angle ∠CBA = ∠P + ∠BCP
=> ∠ CBP = 50o + 20o
=> ∠ CBP = 70o
 
Q.- In Fig. there are two concentric circles with centre O of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP. 

WT_circles test 20

Ans- 

WT_circles test 21

Join OA, OB and OP.
∠OAP =90as the tangent makes a right angle with the radius of the circle at the point of contact.
In ΔOAP, we have,
OP2 = OA2 + AP
OP2 = 52 + 122
=> OP = 13 cm
 
∠ OBP=900 as the tangent makes a right angle with the radius of the circle at the
point of contact.
In ΔOBP, we have,
OP2 = OB2 + BP2
132 = 32 + Bp2
=>  BP2 = 169 - 9 = 160
=>  BP = √160cm =4√10 cm
 
Q.-In the given figure, the pair of tangents A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm, then the radius of the circle is : 
WT_circles test 22
a. 2.5 cm
b. 5 cm
c. 7.5 cm
d. 10 cm
 
Ans-  b. 5 cm
Explanation:
Construction: Joined OA and OB.
Here OA⊥ AP and OB⊥BP and PA⊥PB
Also AP = PB
Therefore, APBO is a square.
=> AP = OA = OB = 5 cm

 

MCQ

1. Number of tangents that can be drawn through a point on the circle is

(a) 3

(b) 2

(c) 1

(d) 0

2. The word tangent came from the Latin word

(a) tang

(b) tangere

(c) tangrant

(d) axyere

3. The word tangent was introduced by

(a) De Moivre

(b) Aryabhata

(c) Disradi

(d) Thomas Fincke

4. Number of tangents to circle which are parallel to a secant is

(a) 1

(b) 2

(c) 3

(d) infinite

5. C(0, r1) and C(0, r2) are two concentric circles with r1 > r2. AB is a chord of (0, r1) touching C(0, r2) at c then

(a) AB = r1

(b) AB = r2

(c) AB = BC

(d) AB = r1 + r2

6. From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm. The radius of circle

(a) 7 cm

(b) 6.5 cm

(c) 5 cm

(d) 9 cm

7. TP and TQ are two tangents to a circle with centre O, so that ∠POQ = 100o, then ∠PTQ is equal to

(a) 60o

(b) 70o

(c) 80o

(d) 90o

8. TP and TQ are two tangents to a circle with centre O, so that ∠POQ = 120o, OPT is equal to

(a) 50o

(b) 60o

(c) 80o

(d) 90o

9. Two concentric circles are of radii 13 cm and 15 cm. The length of chord of a larger circle which touches the smaller circle is

(a) 12 cm

(b) 20 cm

(c) 24 cm

(d) 26 cm

10. A quadrilateral ABCD is drawn to circumscribe a circle. If AB = 12 cm, BC = 15 cm, CD = 14 cm, then AD is equal to

(a) 10 cm

(b) 11 cm

(c) 12 cm

(d) 14 cm

11. A triangle ABC is drawn to circumscribe a circle. If AB = 13 cm, BC = 14 cm and AE = 7 cm, then AC is equal to

(a) 12 cm

(b) 15 cm

(c) 11 cm

(d) 16 cm

12. A right ΔABC right angled at A arawn to circumscribe a circle of radius 5 cm with centre O. If AB = 17 cm, AB = 18 cm, then OC is equal to

 

Please click the below link to access CBSE Class 10 Mathematics Circles Worksheet Set E

More Study Material

CBSE Class 10 Mathematics Chapter 10 Circles Worksheet

We hope students liked the above worksheet for Chapter 10 Circles designed as per the latest syllabus for Class 10 Mathematics released by CBSE. Students of Class 10 should download in Pdf format and practice the questions and solutions given in the above worksheet for Class 10 Mathematics on a daily basis. All the latest worksheets with answers have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their class tests and examinations. Studiestoday is the best portal for Class 10 students to get all the latest study material free of cost.

Worksheet for Mathematics CBSE Class 10 Chapter 10 Circles

Expert teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. If you download the practice worksheet for one chapter daily, you will get higher and better marks in Class 10 exams this year as you will have stronger concepts. Daily questions practice of Mathematics worksheet and its study material will help students to have a stronger understanding of all concepts and also make them experts on all scoring topics. You can easily download and save all revision worksheet for Class 10 Mathematics also from www.studiestoday.com without paying anything in Pdf format. After solving the questions given in the worksheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers

Chapter 10 Circles worksheet Mathematics CBSE Class 10

All worksheets given above for Class 10 Mathematics have been made as per the latest syllabus and books issued for the current academic year. The students of Class 10 can be rest assured that the answers have been also provided by our teachers for all worksheet of Mathematics so that you are able to solve the questions and then compare your answers with the solutions provided by us. We have also provided a lot of MCQ questions for Class 10 Mathematics in the worksheet so that you can solve questions relating to all topics given in each chapter. All study material for Class 10 Mathematics students have been given on studiestoday.

Chapter 10 Circles CBSE Class 10 Mathematics Worksheet

Regular worksheet practice helps to gain more practice in solving questions to obtain a more comprehensive understanding of Chapter 10 Circles concepts. Worksheets play an important role in developing an understanding of Chapter 10 Circles in CBSE Class 10. Students can download and save or print all the worksheets, printable assignments, and practice sheets of the above chapter in Class 10 Mathematics in Pdf format from studiestoday. You can print or read them online on your computer or mobile or any other device. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter.

Worksheet for CBSE Mathematics Class 10 Chapter 10 Circles

CBSE Class 10 Mathematics best textbooks have been used for writing the problems given in the above worksheet. If you have tests coming up then you should revise all concepts relating to Chapter 10 Circles and then take out a print of the above worksheet and attempt all problems. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics

Where can I download latest CBSE Printable worksheets for Class 10 Mathematics Chapter 10 Circles

You can download the CBSE Printable worksheets for Class 10 Mathematics Chapter 10 Circles for latest session from StudiesToday.com

Can I download the Printable worksheets of Chapter 10 Circles Class 10 Mathematics in Pdf

Yes, you can click on the links above and download Printable worksheets in PDFs for Chapter 10 Circles Class 10 for Mathematics

Are the Class 10 Mathematics Chapter 10 Circles Printable worksheets available for the latest session

Yes, the Printable worksheets issued for Class 10 Mathematics Chapter 10 Circles have been made available here for latest academic session

How can I download the Class 10 Mathematics Chapter 10 Circles Printable worksheets

You can easily access the links above and download the Class 10 Printable worksheets Mathematics Chapter 10 Circles for each chapter

Is there any charge for the Printable worksheets for Class 10 Mathematics Chapter 10 Circles

There is no charge for the Printable worksheets for Class 10 CBSE Mathematics Chapter 10 Circles you can download everything free

How can I improve my scores by solving questions given in Printable worksheets in Class 10 Mathematics Chapter 10 Circles

Regular revision of practice worksheets given on studiestoday for Class 10 subject Mathematics Chapter 10 Circles can help you to score better marks in exams

Are there any websites that offer free test sheets for Class 10 Mathematics Chapter 10 Circles

Yes, studiestoday.com provides all latest NCERT Chapter 10 Circles Class 10 Mathematics test sheets with answers based on the latest books for the current academic session

Can test papers for Class 10 Mathematics Chapter 10 Circles be accessed on mobile devices

Yes, studiestoday provides worksheets in Pdf for Chapter 10 Circles Class 10 Mathematics in mobile-friendly format and can be accessed on smartphones and tablets.

Are worksheets for Chapter 10 Circles Class 10 Mathematics available in multiple languages

Yes, worksheets for Chapter 10 Circles Class 10 Mathematics are available in multiple languages, including English, Hindi