CBSE Class 10 Mathematics Circles Worksheet Set 05

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

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.- A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.
 
Sol. Since tangent to a circle is perpendicular to the radius through the point of contact.
Circles notes 9
∴ ∠OTP = 90 0
In right triangle OTP, we have
OP2 = OT2 + PT2
=> 132 = OT2 + 122
=> OT2 = 132 – 122
= (13 – 12) (13 + 12) = 25
=> OT = 5
Hence, radius of the circle is 5 cm.
 
Q.-  Find the length of the tangent drawn from a point whose distance from the centre of a circle is 25 cm. Given that the radius of the circle is 7 cm.
 
Sol. Let P be the given point, O be the centre of the circle and PT be the length of tangent from P. Then, OP = 25 cm and OT = 7 cm.
Circles notes 10
Since tangent to a circle is always
perpendicular to the radius through the point of contact.
∴ ∠OTP=90 0
In right triangle OTP, we have
OP2 = OT2 + PT2
=> 252 = 72 + PT2
=> PT2 = 252 – 72
= (25 – 7) (25 + 7)
= 576
=> PT = 24 cm
Hence, length of tangent from P = 24 cm

 

 
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. (8 cm)
 
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. (60 cm2)
 
3. In the fig. 1, 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. (7.6 cm)
 
CBSE Class 10 Mathematics Circles Worksheet Set E 1
 
SECTION B: 
 
4. 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 d22 = c2 + d12.
 
5. In fig. 2, if CP = 11 cm and BC = 7 cm, then find the length of BR.
 
6. In fig. 3, find the value of x. (4 cm) (60⁰)
CBSE Class 10 Mathematics Circles Worksheet Set E 2
 
 
SECTION C: 
 
7. In fig. 4, if angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then prove that AP = a √3 .
 
8. In the given fig. 5, AB and AC are two tangents to a circle from an external point A. DE is a line segment touching the circle at F and intersecting AB at D and AC at E. Prove that AB = 1/2 (perimeter of ΔADE )
 
9. In fig. 6, ABC is a right triangle in which ∠B ∠ 90 0 . A circle is inscribed in the triangle. If AB = 8 cm and BC = 6 cm, find the radius r of the circle.
CBSE Class 10 Mathematics Circles Worksheet Set E 3
 
SECTION D: 
 
10. In fig.7, a tangent PT and a line segment PBA is drawn to a circle with centre O. If OL ⊥ AB, prove that PA x PB = PT2.
 
11. In fig.8, QR is tangent at Q. PR‖AQ, where AQ is a chord through A and P is a centre, the end point of the diameter AB. Prove that BR is tangent at B.
 
12. Let s denote the semi- perimeter of a triangle ABC in which BC = a, CA = b and AB = c. If a circle touches the sides BC, CA, AB at D, E and F respectively, prove that BD = (s-b).

CBSE Class 10 Mathematics Circles Worksheet Set E 4

 

 

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Chapter 10 Circles Practice Sheet and Solutions for Class 10 Mathematics

Chapter Practice Questions for Class 10 Mathematics

Review targeted practice exercises for Class 10 Mathematics Chapter 10 Circles. Curated to match official CBSE guidelines, these downloadable PDF sheets support daily revision and core concept reinforcement.

Expert Practice Material for Class 10 Mathematics

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FAQs

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

Yes, our CBSE Class 10 Mathematics Circles Worksheet Set 05 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 05?

Yes, we have provided detailed solutions for CBSE Class 10 Mathematics Circles Worksheet Set 05 to help Class 10 and follow the official CBSE marking scheme.

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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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