CBSE Class 10 Maths HOTs Circles

Find CBSE Class 10 Maths HOTs Circles right below. We offer complete High Order Thinking Skills (HOTS) questions and answers for Class 10 Mathematics Chapter 10 Circles. Designed to support your 2026-27 exam session goals, these expert questions match standard curriculum patterns from CBSE, NCERT, and KVS.

Chapter 10 Circles Class 10 Mathematics HOTS with Solutions

Check out these Class 10 Mathematics HOTS Questions to test your advanced knowledge of Mathematics. The detailed answers below will help you practice smarter and build high-level accuracy for your Class 10 tests.

Class 10 Mathematics Chapter 10 Circles Advanced HOTS Questions

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
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Free study material for Mathematics

Higher Order Thinking Skills (HOTS) for Class 10 Mathematics Chapter 10 Circles

Challenging Questions for Class 10 Mathematics Chapter 10 Circles

Master core concepts in Chapter 10 Circles with these targeted Higher Order Thinking Skills (HOTS) problems. Built for Class 10 Mathematics students following the CBSE curriculum, these exercises challenge analytical thinking and improve problem-solving speed.

NCERT-Aligned Solutions and Explanations

Each question in this set is mapped directly to the official NCERT book for Class 10. Review the detailed answer keys provided below each problem to verify your solution steps and correct mistakes early.

Next Steps for Class 10 Mathematics Preparation

Looking for more practice? Explore our complete library of Class 10 Mathematics worksheets, chapter notes, and online mock tests. Everything is provided free of charge to support your academic goals.

FAQs

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 2026-27 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.