CBSE Class 10 Mathematics Circles Worksheet Set 01

Official Class 10 Mathematics Worksheets: Chapter 10 Circles

Access printable practice worksheets for Chapter 10 Circles designed to align with the 2026-27 academic syllabus for Class 10 Mathematics. These structured exercises help students evaluate their conceptual understanding and improve exam readiness.

Chapter-wise Practice Material: Chapter 10 Circles

Access the complete worksheet PDF for Chapter 10 Circles below. Regular practice with these targeted questions builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Question. A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is
(a) 5√2
 (b) 10√2
(c) 5/√2
(d) 10√3

Answer: D

Question. In the given figure, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
(a) 30°
(b) 60°
(c) 90°
(d) 15°

Answer: A

Question. The length of the tangent drawn from a point 8 cm away from the centre of circle of radius 6 cm is
(a) 7 cm
(b) 2 7 cm
(c) 10 cm
(d) 5 cm

Answer: B

Question. From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 15 cm. The radius of the circle is
(a) 9 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm

Answer: A

Question. Two concentric circles of radii 13 cm and 5 cm are given. The length of the chord of the larger circle which touches the smaller circle is
(a) 16 cm
(b) 4 cm
(c) 24 cm
(d) 10 cm

Answer: C

Question. Two concentric circles of radii a and b where a > b, are given, the length of a chord of the larger circle which touches the other circle is
(a) a2 − b2
(b) 2√a2 − b2
(c) a2 + b2
(d) 2√a2 + b2

Answer: B

Question. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle.
The length of the chord CD parallel to XY and at a distance 8 cm from A is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

Answer: D

Question. A tangent to a circle is a line that touches the circle at exactly
(a) two points
(b) three points
(c) one point
(d) none of the options

Answer: C

Question. If the angle between two radii of a circle is 140°, then the angle between the tangents at the ends of the radii is
(a) 90°
(b) 50°
(c) 70°
(d) 40°

Answer: D

Question. The radii of two concentric circles are 16 cm and 10 cm. AB is a diameter of the bigger circle. BD is tangent to the smaller circle touching it at D. Find the length of AD.
(a) 3√130 cm
(b) 2√139 cm
(c) 2√130 cm
(d) 4√139 cm

Answer: B

Question. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to
(a) (3/2)√3 cm
(b) 6 cm
(c) 3 cm
(d) 3√3 cm

Answer: D

Question. How many tangents can a circle have from a point lying inside the circle ?
(a) 2
(b) infinitely many
(c) 1
(d) none of these

Answer: D

Question. Two parallel lines touch the circle at points A and B. If area of the circle is 16p cm2, then AB is equal to
(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 16 cm

Answer: B

Question. If four sides of a quadrilateral ABCD are tangent to a circle, then
(a) AC + AD = BD + CD
(b) AB + CD = BC + AD
(c) AB + CD = AC + BC
(d) AC + AD = BC + DB

Answer: B

Question. From a point P, 10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn. Find the radius of the circle.
Answer: Let O be the centre of the given circle and let P be a point such that
Circles notes 1
OP = 10 cm.
Let PT be the tangent such that PT = 8 cm.
Join OT.
Now, PT is a tangent at T and OT is the
radius through T.
∴ OT ⊥ PT.
In the right ΔOTP, we have
OP2 = OT2 + PT2 [by Pythagoras’ theorem]
=> OT = √OP2 - PT2 =√ (10)2 - (8)2 cm
= √36 cm = 6 cm.
 
Question.  Prove that in two concentric circles, the chord of the larger circle which touches the smaller circle, is bisected at the point of contact.
Answer: Given : Two circles with the same centre O and AB is a chord of the larger circle which touches the smaller circle at P.
Circles notes 2
To prove : AP = BP.
Construction : Join OP.
Proof : AB is a tangent to the smaller circle
at the point P and OP is the radius through P.
∴ OP ⊥ AB.
But, the perpendicular drawn from the centre of a circle to a chord bisects the chord.
∴  OP bisects AB. Hence, AP = BP.
 
 
VERY SHORT ANSWER TYPE QUESTIONS
 
1. In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If ÐOBA = 32°, find the value of x.
CBSE Class 10 Mathematics Circles Worksheet Set A 1
 
2. In the given figure, ABC is a right angled triangle right angled at A, with AB = 6cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.
CBSE Class 10 Mathematics Circles Worksheet Set A 2

3. In the given figure, PT is tangent to the circle at T. If PA = 4 cm and AB = 5 cm, find PT.

CBSE Class 10 Mathematics Circles Worksheet Set A 3

 

4. In the figure, O is the centre of the circle, PQ is tangent to the circle at A. If ÐPAB = 58°, find ÐABQ and ÐAQB.
CBSE Class 10 Mathematics Circles Worksheet Set A 4
 
5. In figure, a circle touches the side BC of DABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of DABC.
CBSE Class 10 Mathematics Circles Worksheet Set A 5
6. A tangent PT is drawn parallel to a chord AB as shown in figure. Prove that APB is an isosceles triangle.
CBSE Class 10 Mathematics Circles Worksheet Set A 6
 
7. In figure, XP and XQ are two tangents to a circle with centre O from a point X outside the circle. ARB is tangent to circle at R. Prove that XA + AR = XB + BR.

CBSE Class 10 Mathematics Circles Worksheet Set A 7

 
 
8. In fig, if ÐATO = 40°, find ÐAOB.
CBSE Class 10 Mathematics Circles Worksheet Set A 8

 

9. In fig., CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR. 
CBSE Class 10 Mathematics Circles Worksheet Set A 9
 
10. In fig., DABC is circumscribing a circle. Find the length of BC.
CBSE Class 10 Mathematics Circles Worksheet Set A 10
 
 

Please click on below link to download CBSE Class 10 Mathematics Circles Worksheet Set A

Free study material for Mathematics

Practice Worksheet and Study Resources for Class 10 Mathematics Chapter 10 Circles

Download Practice Sheet: Chapter 10 Circles (Class 10 Mathematics)

Access structured practice worksheets for Chapter 10 Circles designed in alignment with the latest CBSE curriculum for Class 10 Mathematics. These printable problem sets help students build accuracy and prepare effectively for school tests.

Concept Clarification for Chapter 10 Circles

Built using the official NCERT book for Class 10 Mathematics, these practice materials provide reliable academic guidance. Pair your practice with our recommended NCERT solutions to master optimal problem-solving approaches.

Additional Study Resources for Class 10 Mathematics

Follow up your worksheet practice by attempting the interactive online Mathematics MCQ test for this chapter to evaluate your execution speed. All platform resources are free to access.

FAQs

Where can I download the latest PDF for CBSE Class 10 Mathematics Circles Worksheet Set 01?

You can download the teacher-verified PDF for CBSE Class 10 Mathematics Circles Worksheet Set 01 from StudiesToday.com. These practice sheets for Class 10 Mathematics are designed as per the latest CBSE academic session.

Are these Mathematics Class 10 worksheets based on the 2026-27 competency-based pattern?

Yes, our CBSE Class 10 Mathematics Circles Worksheet Set 01 includes a variety of questions like Case-based studies, Assertion-Reasoning, and MCQs as per the 50% competency-based weightage in the latest curriculum for Class 10.

Do you provide solved answers for CBSE Class 10 Mathematics Circles Worksheet Set 01?

Yes, we have provided detailed solutions for CBSE Class 10 Mathematics Circles Worksheet Set 01 to help Class 10 and follow the official CBSE marking scheme.

How does solving CBSE Class 10 Mathematics Circles Worksheet Set 01 help in exam preparation?

Daily practice with these Mathematics worksheets helps in identifying understanding gaps. It also improves question solving speed and ensures that Class 10 students get more marks in CBSE exams.

Is there any charge for the Class 10 Mathematics practice test papers?

All our Class 10 Mathematics practice test papers and worksheets are available for free download in mobile-friendly PDF format. You can access CBSE Class 10 Mathematics Circles Worksheet Set 01 without any registration.