CBSE Class 10 Mathematics Circles Worksheet Set 06

Practice Worksheets for Class 10 Mathematics: Chapter 10 Circles

Review targeted practice sets for Class 10 Mathematics Chapter 10 Circles. Built according to official educational guidelines for the 2026-27 academic year, these downloadable worksheets support daily revision and core concept reinforcement.

Practice Chapter 10 Circles Worksheets for Class 10 Mathematics

View or download the dedicated Chapter 10 Circles practice resource below. Engaging with these objective and subjective questions daily ensures continuous academic progress and mastery of the 2026-27 curriculum.

CIRCLES
 
Q.- In Fig., if AB = AC, prove that BE = EC
Circles notes 11
 
Sol. Since tangents from an exterior point to a circle are equal in length 
∴ AD = AF     [Tangents from A]
BD = BE       [Tangents from B]
CE = CF       [Tangents from C]
Now,
AB = AC
=> AB – AD = AC – AD
[Subtracting AD from both sides]
=> AB – AD = AC – AF [Using (i)]
=> BD = CF    => BE = CF [Using (ii)]
=> BE = CE [Using (iii)]
 
Q.- In fig. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle.
Circles notes 12
Prove that, XA + AR = XB + BR.
 
Sol. Since lengths of tangents from an exterior
point to a circle are equal.
∴ XP = XQ      .... (i) [From X]
AP = AR         .... (ii) [From A]
BQ = BR         .... (iii) [From B]
Now, XP = XQ
=> XA + AP = XB + BQ
=> XA + AR = XB + BR
[Using equations (i) and (ii)]
 
SECTION A:
 
1. A line touches a circle of radius 4 cm. Another line is drawn which is tangent to the circle. If the two lines are parallel then find the distance between them.
 
2. From a point P, which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR are drawn to the circle. Find the area of the quadrilateral PQOR.
 
3. In fig 1, if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then find∠POQ.
 
4. In the figure 2, QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find the length of QR.
 
5. In fig. 3, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm, BC = 7 cm, then find the length of BR.
CBSE Class 10 Mathematics Circles Worksheet Set F1
 
6. Point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then find the radius of the circle.
 
7. TP and TQ are two tangents to a circle with centre O such that ∠POQ = 110⁰. Then find ∠PTQ.
 
8. In the figure , QR is a common tangent to given circle which meet at T. Tangent at T meets QR at P. If QP = 3.8 cm, then find the length of QR.
CBSE Class 10 Mathematics Circles Worksheet Set F2
 
9. If the angle between two radii of a circle is 100⁰, find the angle between the tangents at the ends of the radii.
 
10. From a point P which is at a distance of 13 cm from the center of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then find the area of the quadrilateral PQOR.
 
SECTION B :
 
1. Two concentric circles of radii a and b , where a>b are given. Find the length of chord of the larger circle which touches the smaller circle.
 
2. If d1, d2(d2>d1) be diameters of two concentric circles, c be the length of a chord of the circle which is tangent to the other circle, prove that d2 2 = c2 + d12.
 
3. If two tangents inclined at an angle 60⁰ are drawn to a circle of radius 3 cm, find the length of each tangent.
 
4. PA and PB are two tangents drawn from an external point P to a circle with centre O. If OP is equal to diameter of the circle, prove that ΔABP is equilateral.
 
5. A circle touches the side AC of ΔABC at P, touches BC at Q and AB at R. Show thatAC + AR = BC + BR.
CBSE Class 10 Mathematics Circles Worksheet Set F3
 
6. If two tangents inclined at an angle 60⁰ are drawn to a circle of radius 3 cm, find the length of each tangent.
 
7. Two parallel lines touch a circle at points A and B separately. If area of the circle is 25 cm2, then find the length of AB.
 
8. In figure, if CP = 11 cm and BC = 7 cm, then find the length of BR.
CBSE Class 10 Mathematics Circles Worksheet Set F4
 
9. In the given figure , BOA is a diameter of a circle and the tangent at a point P meets BA produced at T. If ∠PBO = 30°, what is the measure of ∠PTA?
CBSE Class 10 Mathematics Circles Worksheet Set F5
 
10. In fig , a tangent PT is drawn parallel to a chord AB of a circle, as shown in given figure. Prove that APB is an isosceles triangle.
CBSE Class 10 Mathematics Circles Worksheet Set F6
 
SECTION C: 
 
1. In figure, a triangle ABC is drawn to circumscribe a circle of radius 10 cm such that the segments BP and PC into which BC is divided by the point of contact P, are of lengths 15 cm and 20 cm respectively. If the area of ΔABC is 525 cm2, then find the lengths of sides AB and AC.
CBSE Class 10 Mathematics Circles Worksheet Set F7
 
2. If angle between two tangents PT and QT drawn from a point T to a circle of radius r and centre O is 60⁰, then prove that PT = 3r.

 

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Exam Preparation Worksheet for Class 10 Mathematics Chapter 10 Circles

CBSE Practice Material: Class 10 Mathematics Chapter 10 Circles

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.

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FAQs

Where can I download the latest PDF for CBSE Class 10 Mathematics Circles Worksheet Set 06?

You can download the teacher-verified PDF for CBSE Class 10 Mathematics Circles Worksheet Set 06 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 06 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 06?

Yes, we have provided detailed solutions for CBSE Class 10 Mathematics Circles Worksheet Set 06 to help Class 10 and follow the official CBSE marking scheme.

How does solving CBSE Class 10 Mathematics Circles Worksheet Set 06 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.

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