CBSE Class 10 Maths HOTs Circles

Refer to CBSE Class 10 Maths HOTs Circles. We have provided exhaustive High Order Thinking Skills (HOTS) questions and answers for Class 10 Mathematics Chapter 10 Circles. Designed for the 2025-26 exam session, these expert-curated analytical questions help students master important concepts and stay aligned with the latest CBSE, NCERT, and KVS curriculum.

Chapter 10 Circles Class 10 Mathematics HOTS with Solutions

Practicing Class 10 Mathematics HOTS Questions is important for scoring high in Mathematics. Use the detailed answers provided below to improve your problem-solving speed and Class 10 exam readiness.

HOTS Questions and Answers for Class 10 Mathematics Chapter 10 Circles

Class 10 Circles HOTs (1)

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Please refer to link below to download pdf file ofCBSE Class 10 Hots Question Class 10 Circles HOTs(1)

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Please refer to link below to download pdf file of CBSE Class 10 Hots Question CBSE Class 10 Circles HOTs (2)

HOTS Level 1 And Level2

2 Mark Questions

Q1In the given figure PQ,PR and AB are tangents at points Q,R and S respectively of a circle. If PQ =8 cm .Find the Perimeter of triangle

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Sol. AQ=AS
BR=BS
PQ=PR=8cm
Perimeter of Δ APB =AP+AB+PB
= PQ-AQ+AS+BS+PR-BR
=PQ+PR
=8+8=16cm

Q2. PT is a Tangent to circle with centre O. OT=56cm,TP=90 cm Find OP
Sol. A Tangnt to the Circle is perpendicularto the radius at the point of contact So, OT TP
Implies ΔOTP is a rt angle Δ
Therefore Op2=OT2+TP2
562+902= 3136+8100 

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OC > OP (∵ C lies outside the circle)
This is true for all positions of C on AB. 
Thus, OP is the shortest distance between point P and line segment AB.
Hence, OP ⊥ AB.
 
Q2.Theorem :Tangents drawn to a circle from an external point are equal in length. 
Given:- Two tangents AB and AC from an external point A to points B and C on a circle. 
To prove: AB = AC

 

 Construction: Join OA, OB and OC. Proof:In triangles OAB and OAC, 
∠OBA = 90⁰ (Radius OB ⊥ Tangent AB at B) 
∠OCA = 90⁰ (Radius OC ⊥ Tangent AC at C) 
In triangles OBA and OCA, 
∠OBA = ∠OCA = 90⁰ 
OB = OC (Radii of the same circle)  
OA = OA (Common side)  
Thus, ΔOBA =̃ ΔOCA (RHS congruence rule)  
Hence, AB = AC (By C.P.C.T)  
Q3. In figure 5, the common tangents AB and CD to two circles with centres O and O’ intersect in E. Prove that the points O , E and O’ are collinear.
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In figure 5, the common tangents AB and CD to two circles with centres O and O’ intersect in E. Prove that the points O , E and O’ are collinear. 
Sol. By the property of tangents drawn to a circle from an external point, we have  
∠1= ∠2 ……………….(i)

 ∠3= ∠4 ……………….(ii) 

Also ∠AED = ∠CEB (Vertically opposite angles) …………(iii) 
Adding (i),(ii) and (iii), we get 
∠1+ ∠3+ ∠AED= ∠2+ ∠4+ ∠CEB 
But (∠1+ ∠3+ ∠AED) + (∠2+ ∠4+ ∠CEB) = 360° , (angles at a point) 
∴we must have 
∠1+ ∠3+ ∠AED= ½ (360°) = 180° 
⇒ EO and EO’ are collinear 
⇒ O, E and O’ lie in the same line 
Q4.From the given fig. A Circle touches all four sides of Quadrilateral ABCD. Prove that AB+CD=BC+DA  
Sol. From the fig. AS=AP, SD=DR , PB=BQ, CR=CQ(Tangents) AS+SD+BQ+CQ=AP+PB+CR+DR 
AD+BC=AB+CD 
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Q5. Prove that the ||gm circumscribing a circle isa rhombus  
Sol. Given: ABCD ||gm touching the circle at M,N,P,Q To prove: ABCD is a rhombus 
Proof: AQ=AM  
DQ=DP BN=MB NC=PC 
Adding the above we get 
AD+BC=AB+CD AD=BC and AB=CD AD=AB=BC=CD 
It is a rhombus
 
MORE QUIESTION
 
Cricle
Key points
 
1. Tangent to a circle : It is a line that intersects the circle at only one point.
 
2. There is only one tangent at a point of the circle.
 
The proofs of the following theorems can be asked in the examination :-
(i) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
(ii) The lengths of tangents drawn from an external point to a circle are equal.
 
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Please refer to link below for CBSE Class 10 Mathematics HOTs Circles Set A.

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2.  A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R respectively as shown in figure. 
 Show that AQ=1/2 (perimeter of triangle ABC)

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ADDITIONAL QUESTION
CBSE_ Class_10_Mathematics_Circle_1
CBSE_ Class_10_Mathematics_Circle_2
Chapter 01 Real Numbers
CBSE Class 10 Maths HOTs Number Systems
Chapter 02 Polynomials
CBSE Class 10 Maths HOTs Polynomials
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Maths HOTs Pair Of Linear Equations In Two Variables
Chapter 04 Quadratic Equation
CBSE Class 10 Maths HOTs Quadratic Equations
Chapter 05 Arithmetic Progressions
CBSE Class 10 Maths HOTs Arithmetic Progressions
Chapter 06 Triangles
CBSE Class 10 Maths HOTs Similar Triangles
Chapter 07 Coordinate Geometry
CBSE Class 10 Maths HOTs Co-Ordinate Geometry
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Maths HOTs Trigonometry
Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Maths HOTs Heights And Distances
Chapter 10 Circles
CBSE Class 10 Maths HOTs Circles
Chapter 11 Areas Related to Circles
CBSE Class 10 Maths HOTs Area related to Circle
Chapter 12 Surface Areas and Volumes
CBSE Class 10 Maths HOTs Conversion Of Solids
CBSE Class 10 Maths HOTs Mensuration
CBSE Class 10 Maths HOTs Surface Area and Volumes
Chapter 13 Statistics
CBSE Class 10 Maths HOTs Statistics
Chapter 14 Probability
CBSE Class 10 Maths HOTs Probability
More HOTs for Class 10 Mathematics
CBSE Class 10 Maths HOTs Question Bank Set B
CBSE Class 10 Maths HOTs Question Bank Set C
CBSE Class 10 Maths HOTs Question Bank Set D
CBSE Class 10 Maths HOTs Question Bank Set E
~ Class 10 Mathematics (Old Chapters)
CBSE Class 10 Mathematics HOTs Constructions

Important Practice Resources for Class 10 Mathematics

HOTS for Chapter 10 Circles Mathematics Class 10

Students can now practice Higher Order Thinking Skills (HOTS) questions for Chapter 10 Circles to prepare for their upcoming school exams. This study material follows the latest syllabus for Class 10 Mathematics released by CBSE. These solved questions will help you to understand about each topic and also answer difficult questions in your Mathematics test.

NCERT Based Analytical Questions for Chapter 10 Circles

Our expert teachers have created these Mathematics HOTS by referring to the official NCERT book for Class 10. These solved exercises are great for students who want to become experts in all important topics of the chapter. After attempting these challenging questions should also check their work with our teacher prepared solutions. For a complete understanding, you can also refer to our NCERT solutions for Class 10 Mathematics available on our website.

Master Mathematics for Better Marks

Regular practice of Class 10 HOTS will give you a stronger understanding of all concepts and also help you get more marks in your exams. We have also provided a variety of MCQ questions within these sets to help you easily cover all parts of the chapter. After solving these you should try our online Mathematics MCQ Test to check your speed. All the study resources on studiestoday.com are free and updated for the current academic year.

Where can I download the latest PDF for CBSE Class 10 Maths HOTs Circles?

You can download the teacher-verified PDF for CBSE Class 10 Maths HOTs Circles from StudiesToday.com. These questions have been prepared for Class 10 Mathematics to help students learn high-level application and analytical skills required for the 2025-26 exams.

Why are HOTS questions important for the 2026 CBSE exam pattern?

In the 2026 pattern, 50% of the marks are for competency-based questions. Our CBSE Class 10 Maths HOTs Circles are to apply basic theory to real-world to help Class 10 students to solve case studies and assertion-reasoning questions in Mathematics.

How do CBSE Class 10 Maths HOTs Circles differ from regular textbook questions?

Unlike direct questions that test memory, CBSE Class 10 Maths HOTs Circles require out-of-the-box thinking as Class 10 Mathematics HOTS questions focus on understanding data and identifying logical errors.

What is the best way to solve Mathematics HOTS for Class 10?

After reading all conceots in Mathematics, practice CBSE Class 10 Maths HOTs Circles by breaking down the problem into smaller logical steps.

Are solutions provided for Class 10 Mathematics HOTS questions?

Yes, we provide detailed, step-by-step solutions for CBSE Class 10 Maths HOTs Circles. These solutions highlight the analytical reasoning and logical steps to help students prepare as per CBSE marking scheme.