CBSE Class 10 Maths HOTs Circles

Please refer to CBSE Class 10 Maths HOTs Circles. Download HOTS questions and answers for Class 10 Mathematics. Read CBSE Class 10 Mathematics HOTs for Chapter 10 Circles below and download in pdf. High Order Thinking Skills questions come in exams for Mathematics in Class 10 and if prepared properly can help you to score more marks. You can refer to more chapter wise Class 10 Mathematics HOTS Questions with solutions and also get latest topic wise important study material as per NCERT book for Class 10 Mathematics and all other subjects for free on Studiestoday designed as per latest CBSE, NCERT and KVS syllabus and pattern for Class 10

Chapter 10 Circles Class 10 Mathematics HOTS

Class 10 Mathematics students should refer to the following high order thinking skills questions with answers for Chapter 10 Circles in Class 10. These HOTS questions with answers for Class 10 Mathematics will come in exams and help you to score good marks

HOTS Questions Chapter 10 Circles Class 10 Mathematics with Answers

Class 10 Circles HOTs (1)

CBSE_Class_10_Maths_Circles_1..

CBSE_Class_10_Maths_Circles_2..

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

CBSE_Class_10_Maths_Circles_1

CBSE_Class_10_Maths_Circles_2

CBSE_Class_10_Maths_Circles_3

CBSE_Class_10_Maths_Circles_4

CBSE_Class_10_Maths_Circles_5

CBSE_Class_10_Maths_Circles_6

CBSE_Class_10_Maths_Circles_7

CBSE_Class_10_Maths_Circles_8

CBSE_Class_10_Maths_Circles_9

CBSE_Class_10_Maths_Circles_10

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

class_10_maths_hot_011

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 

class_10_maths_hot_09

class_10_maths_hot_010

 

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.
CBSE_Class_10_maths_circle_Set_A_2

 

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 
CBSE_Class_10_maths_circle_Set_A_3

 

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.
 
CBSE_ Class_10_Mathematics_Circle_1
CBSE_ Class_10_Mathematics_Circle_2
CBSE_ Class_10_Mathematics_Circle_3
CBSE_ Class_10_Mathematics_Circle_4
CBSE_ Class_10_Mathematics_Circle_5
CBSE_ Class_10_Mathematics_Circle_6

Please refer to link below for CBSE Class 10 Mathematics HOTs Circles Set A.

class_10_maths_hot_2 

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)

CBSE_Class_10_maths_circle_1

CBSE_Class_10_maths_circle_2
CBSE_Class_10_maths_circle_3
CBSE_Class_10_maths_circle_4
 
CBSE_Class_10_maths_circle_7
CBSE_Class_10_maths_circle_8
CBSE_Class_10_maths_circle_9
CBSE_Class_10_maths_circle_10 
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 Constructions
CBSE Class 10 Mathematics HOTs Constructions
Chapter 12 Areas Related to Circles
CBSE Class 10 Maths HOTs Area related to Circle
Chapter 13 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 14 Statistics
CBSE Class 10 Maths HOTs Statistics
Chapter 15 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
Tags
CBSE HOTs Question
CBSE Class 10 Mathematics HOTs Question
CBSE Class 10 Mathematics pdf HOTs Question
Class 10 Mathematics HOTs Question pdf
CBSE Class 10 Mathematics
Mathematics Class 10 HOTs Question
CBSE Class 10 Mathematics Chapter HOTs Question
HOTs Question for Class 10 Mathematics
NCERT Class 10 Mathematics HOTs

HOTS for Chapter 10 Circles Mathematics Class 10

Expert teachers of studiestoday have referred to NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 HOTS. If you download HOTS with answers for the above chapter you will get higher and better marks in Class 10 test and exams in the current year as you will be able to have stronger understanding of all concepts. High Order Thinking Skills questions practice of Mathematics and its study material will help students to have stronger understanding of all concepts and also make them expert on all critical topics. You can easily download and save all HOTS for Class 10 Mathematics also from www.studiestoday.com without paying anything in Pdf format. After solving the questions given in the HOTS which have been developed as per latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers. We have also provided lot of MCQ questions for Class 10 Mathematics in the HOTS so that you can solve questions relating to all topics given in each chapter. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter

Where can I download latest CBSE HOTS for Class 10 Mathematics Chapter 10 Circles

You can download the CBSE HOTS for Class 10 Mathematics Chapter 10 Circles for latest session from StudiesToday.com

Are the Class 10 Mathematics Chapter 10 Circles HOTS available for the latest session

Yes, the HOTS issued by CBSE for Class 10 Mathematics Chapter 10 Circles have been made available here for latest academic session

What does HOTS stand for in Class 10 Mathematics Chapter 10 Circles

HOTS stands for "Higher Order Thinking Skills" in Chapter 10 Circles Class 10 Mathematics. It refers to questions that require critical thinking, analysis, and application of knowledge

How can I improve my HOTS in Class 10 Mathematics Chapter 10 Circles

Regular revision of HOTS given on studiestoday for Class 10 subject Mathematics Chapter 10 Circles can help you to score better marks in exams

Are HOTS questions important for Chapter 10 Circles Class 10 Mathematics exams

Yes, HOTS questions are important for Chapter 10 Circles Class 10 Mathematics exams as it helps to assess your ability to think critically, apply concepts, and display understanding of the subject.