CBSE Class 10 Mathematics Circles Worksheet Set 03

Official Class 10 Mathematics Worksheets: 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.

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.

Q.- A circle touches the side BC of a ΔABC at P,and touches AB and AC produced at Q and R respectively, as shown in the figure.

Circles notes 5

Show that AQ = 1/2 (perimeter of ΔABC)
 
Sol. We know that the lengths of tangents drawn
from an exterior point to a circle are equal.
∴ AQ = AR .... (i) [tangents from A]
BP = BQ .... (ii) [tangents from B]
CP = CR .... (iii) [tangents from C]
Perimeter of ΔABC
= AB + BC + AC
= AB + BP + CP + AC
= AB + BQ + CR + AC [using (ii) and (iii)]
= AQ + AR
= 2AQ [using (i)].
Hence, AQ = 1/2 (perimeter of ΔABC)
 
Q.-  Prove that there is one and only one tangent at any point on the circumference of a circle.
 
Sol. Let P be a point on the circumference of a circle with centre O. If possible, Let PT and PT' be two tangents at a point P of the circle.
Now, the tangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ OP ⊥PT and similarly, OP⊥PT'
=> ∠OPT = 90° and ∠OPT' = 90°
=> ∠OPT = ∠OPT'
This is possible only when PT and PT' coincide. Hence, there is one and only one tangent at any point on the circumference of a circle.
 
Q.- A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure.
Circles notes 6
Prove that AB + CD = AD + BC
 
Sol. We known that the lengths of tangents drawn from an exterior point to a circle are equal.
∴ AP = AS ....(i) [tangents from A]
BP = BQ ....(ii) [tangents from B]
 CR = CQ ....(iii) [tangents from C]
 DR = DS ....(iv) [tangents from D]
∴ AB + CD = (AP + BP) + (CR + DR)
= (AS + BQ) + (CQ + DS)
[using (i), (ii), (iii), (iv)]
= (AS + DS) + (BQ + CQ)
= (AD + BC).
Hence, (AB + CD) = (AD + BC)
 

CBSE Class 10 Mathematics Circles Worksheet Set C 1

CBSE Class 10 Mathematics Circles Worksheet Set C 2

CBSE Class 10 Mathematics Circles Worksheet Set C 3

 

 

 

44CBSE Class 10 Mathematics Circles Worksheet Set C 4

 

 

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

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Download CBSE Practice Material: Class 10 Mathematics Chapter 10 Circles

Chapter 10 Circles Printable Worksheet 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.

How to Use These Practice Sheets

Each worksheet is structured around standard CBSE textbooks, allowing students to check their working steps and correct mistakes early in their revision.

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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 03 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.

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Yes, we have provided detailed solutions for CBSE Class 10 Mathematics Circles Worksheet Set 03 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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