CBSE Class 10 Mathematics HOTs Constructions

Read CBSE Class 10 Mathematics HOTs Constructions below. Access comprehensive High Order Thinking Skills (HOTS) questions with answers for Class 10 Mathematics Chapter 11 Constructions. Tailored for the 2026-27 exam session, these analytical problems help Class 10 students understand deep concepts based on the latest CBSE, NCERT, and KVS syllabus.

Analytical Questions: Chapter 11 Constructions (Class 10 Mathematics)

Every Class 10 Mathematics student should practice these HOTS Questions to tackle difficult exam problems. Use the provided solutions to improve your critical thinking and boost your overall performance in Class 10.

Class 10 Mathematics Chapter 11 Constructions Advanced HOTS Questions

CBSE Class 10 Constructions HOTs. Higher Order Thinking Skills (HOTS) are part of the CBSE syllabus and form part of examinations. Students are requested to learn the HOTs for various subjects to score better in examinations, This portal has collection of important HOTs for all subjects and classes which have been made by experienced school teachers. Students should download and learn the HOTS.

TOPIC- Constructions (Class- X)

1. Draw a triangle ABC with sides BC = 6.3cm, AB = 5.2cm and ÐABC = 60° . Then construct a triangle whose sides are 43 times the corresponding sides of Δ ABC.
Solution: Steps of construction
1. Draw a line segment BC = 6.3cm
2. At B make < CBX = 60°
3. With B as centre and radius equal to 5.2 cm, draw an arc intersecting BX at A
4. Join AC, Then ABC is the required triangle
5. Draw any ray by making an acute angle with BC on the opposite side to the vertex A
6. Locate the points B1, B2, B3, B4 on BY so thatB1B2= B2B3= B3B4,
7. Join B3 to C and draw al line through B4 parallel to B3 C intersecting the extended line segment BC at C’.
8. Draw a line through C’ parallel to CA intersecting the extended line segment BA at A’ Thus A’BC’ is the required triangle.

class_10_maths_hot_03

2. Let ABC be a right triangle in which AB = 6cm, BC = 8cm and ÐB = 90° BD is the perpendicular from B on AC. The circle through B,C and D is drawn construct the tangents from A to this circle.
Solution: Steps of construction
1. Draw DABC with BC = 8cm, AB = 6cm and <B = 90°
2. Draw perpendicular BD from B to AC

3. Let O be the mid point of BC. Draw a circle with centre O and radius OB = OC. This circle will pass through the point D
4. Join AO and bisect AO
5. Draw a circle with centre O' and O' Aas radius cuts the previous circle at B and P
6. Join AP, AP and AB are required tangents drawn from A to the circle passing through B,C and D.

class_10_maths_hot_04

3. Draw a circle of radius 4 cm . Take a point P outside the circle. Without using the centre of the circle, draw two tangents to the circle from point P.
Solution: Steps of Construction:
i) Draw a line segment of 4 cm.
ii) Take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.
iii) Produce AP to C such that AP=CP
iv) Draw a semi-circle with CB as diameter.
v) Draw PD perpendicular to CB, intersecting the semi-circle at D.
vi) With P as centre and PD as radius draw arcs to intersect the given circle at and T’.

vii) Join PT and PT’. Then, PT and PT’ are the required tangents.

CBSE_Class_10_maths_construction_1

4. Construct a triangle ABC in which BC = 6cm, <A=600 and the attitude through A is 4.5cm. Measure the length of median through A. Write the steps of construction.
Solution:-
CBSE_Class_10_maths_construction_2
Steps of Construction: 
i) <CBP=600 BC = 6cm is drawn and is made downwards with BC of any length.
ii)<PBE=900 is drawn
iii) Perpendicular bisector RQ of BC is drawn which cut BC at M. and
intersect BE at O.
iv) Taking O as centre and OB as radius, a circle is drawn.
v)  ML = 4.5cm is cut from RQ.
vi) A line XY, parallel to BC is drawn through L to intersect the circle at A and A'.
AB, AC, A’B and A’C are joined.
ABC and A’BC are the required triangle
Median AM = A'M = 5.5cm (app.) 
 
5. Construct a triangle ABC in which BC = 5cm, <A700 and median AD through A is of length 3.5cm. Also, determine the length of the altitude drawn from A on the side BC (Write the steps of construction also).
 
Solution:-

CBSE_Class_10_maths_construction_3 

Steps Of Construction: 
i) BC = 5cm is drawn and is constructed downwards. ii)  BX is drawn perpendicular to BY. 
iii) Q is drawn perpendicular bisector if BC intersecting BX at O and cutting BC at E.  
iv) Taking O as a centre and OB as radius, a circle is drawn.
v)  Taking E as centre and radius equal to 3.5cm, arc is drawn to cut the circle at A. 
vi) AC and AB are joined 
vii)AD is drawn perpendicular to BC from A to cut BC at D. viii) By measuring we find that AD = 3cm. 
 
6. ΔABC˜ Draw a  to a equilateral ΔPQR with side 5cm such that each of its sides is 6/7th of the corresponding side of ΔPQR Also draw the circumcircle of ΔABC .

Solution:-

 CBSE_Class_10_maths_construction_4

Steps Of Construction:  
i) A ray QX is drawn making any angle with QR and opposite to P. 
ii)  Starting from Q, seven equal line segments QQ1, Q1R2, Q2Q3, Q3Q4, Q4Q5, Q5Q6, Q6Q7 are cut of from QX. 
iii) RQ7 is joined and a line CQ6 is drawn parallel to RQ4 to intersect QR at C. 
iv) Line CA is drawn parallel to PR. 
ABC is the required triangle.  
 
7. Construct a triangle ABC in which BC = 6cm, <=A600and median AD = 5cm. Also construct another triangle BPQ similar to triangle BCA such that the side BP = 3/2BC. Solution:-

 CBSE_Class_10_maths_construction_5

Steps Of Construction:  
i)   A line segment BC of length 6cm is drawn.
ii)  At B, <CBX=600is drawn on downwards.
iii) At B, CBSE_Class_10_maths_construction_11 is drawn 
iv) Perpendicular bisector of BC is drawn which intersect BY at O and BC at D. 
v)  Taking O as a center and OB as a radius a circle passing through B and C is drawn. 
vi) Taking D as a centre and radius 5cm an arc is drawn to intersect the circle at A. 
vii)AB and AC are joined. The required triangle is ABC. 
viii) Taking C as centre and CD as radius an arc is drawn to intersect BC produced at P such that BP = 3/2BC. 
ix) Through P, PQ is drawn parallel to CA meeting BA produced at Q.
x)  BPQ is the required triangle similar to triangle BCA.
 
8. Construct a quadrilateral ABCD in which AB = 2.5cm, BC = 3.5cm, AC = 4.2cm, CD = 3.5cm and AD = 2.5cm. Construct another quadrilateral AB’C’D’ with diagonal AC’ = 6.3cm such that it is similar to quadrilateral ABCD.
 
Solution:-

CBSE_Class_10_maths_construction_6

 

Steps Of Construction:  
i) A line segment Ac = 4.2cm is drawn. 
ii)  With A as a centre and radius 2.5cm, two arcs, one above AC and one below AC are drawn. 
iii) With C as centre and radius 3.5cm, two arcs arc drawn intersecting previous arcs at B and D./li> 
iv) AB, AD, BC and CD are joined ABCD is the required quadrilateral. 
v)  Taking A as a centre and radius 6.3cm an arc is drawn to intersect AC produced at C’. 
vi) Through C’, C’B’ and C’D’ are drawn parallel to CB and CD respectively. 
AB’C’D’ is the required quadrilateral similar to ABCD.
 
MORE QUESTION
 
Constructions
Key points
1. Construction should be neat and clean and as per scale given in question.
2. Steps of construction should be provided only to those questions where it is mentioned.
 
Questions
 
3 marks questions
Q. 1 Draw a line segment 14 cm long and find a point which divideds it in the 4 : 3. Also write the steps of construction.
 
Q. 2 Divide a 8 cm long line segment in the ratio 1 : 3. Also write the steps of construction.
 
Q. 3 Draw a line segment AB = 6.5 cm and find the point 'x' on it which divides it in the ratio 1 : 4. By actual measurement find AX / BX .
 
Q. 4 Draw a line segment AB = 9 cm and locate a point C on AB such that 4× AC = 5× BC.
 
Q. 5 Construct a circle C (0, 3). Take a point P at a distance of 6.5 cm from the centre. Construct the tangents to the circle from point P. Also write the steps of construction.
 
Q. 6 Mark a point P outside a circle C (0, 2.4) such that OP = 5 cm. Draw two tangents PA and PB to the circle from point P. Also write the steps of construction.
 
Q. 7 Draw a line segment BC = 7.5 cm. Find the point P on BC such that BP : PC = 2 : 3. Measure the length of BP and PC. Also write the steps of construction.
 
Q. 8 Construct a triangle AB'C' similar to given ΔABC such that each of its sides is 2 /3 rd of the corresponding sides of the ΔABC. It is given that AB = 6 cm, BC = 5 cm and AC = 6 cm. Also write the steps of construction.
 
Q. 9 Construct a triangle X 'YZ ' similar to given triangle XZY with its sides 1½ times that of the corresponding sides of a ΔXYZ . If is given that XY = 5 cm, YX = 7.4 cm and ∠XYZ = 740 . Also write the steps of constructions.
 
Q. 10 Construct an isosecles triangle with base 7 cm and vertical angle 1200 . Construct a triangle similar to given triangle with its corresponding sides being 4/3 times those of given triangle.
 
Q. 11 Construct a triangle A'BC' similar to given ΔABC with its sides equal to 1/3rd of its corresponding sides. It is given that ∠B = 900 , AB = 6 cm and BC = 8 cm.
 
Q. 12 Draw ΔABC with BC = 8 cm, ∠ABC = 450 and ∠BAC = 1050 . Then construct a triangle whose sides are 2 / 3 times the corresponding sides of the ΔABC .
 
Q. 13 Draw two tangents from the end points of diameter if the radius of the circle is 3 cm. Are these tangents parallel? Give reason.
 
Q. 14 Construct ΔPQR in which PQ = 7 cm, ∠Q = 500 and altitude RM to PQ is equal to 4.5 cm. Construct a ΔP'QR' similar to ΔPQR having each of its side 2/3 rd of the corresponding sides of ΔPQR . Also write the steps of construction.
 
Q. 15 Construct a ΔPQR in which PQ = 6 cm, ∠Q = 700 and altitude PS = 4 cm. Also construct a ΔPBC ∼ ΔPQR such that each side of ΔPBC is 1.8 times that of the corresponding sides of ΔPQR .
 
Q. 16 Draw a circle C (0, 2.5) P and Q are points on the circle such that ∠POQ =1200 . Construct tangents to the circle at P and Q to meet at a point R. Write measure ∠PRQ. What is the value of ∠POQ +∠PRQ ?
 
Q. 17 Draw a circle with centre D and radius 3 cm. Draw two tangent segments XY and XY ' from an exterior point X such that ∠YXY ' = 450 . Also write the steps of constructions.
 
Q. 18 Construct an equilateral triangle PQR with side 6 cm. Construct another triangle ΔP'QR' ∼ ΔPQR such that  PQ/P'Q = 1/' 2 . Is ΔP'QR' an equilateral triangle?
 
Q. 19 Draw a circle of radius 4.2 cm. Extend the diameter to both the sides to the points P and Q such that each point is at a distance of 7 cm from the centre. Draw the tangent to the circle from these two points P and Q?
 
Q. 20 Draw a line segment AB = 9 cm. With A and B as centres draw circles of radius 5 cm and 3 cm respectively. Construct tangent to each circle from the centre of the other circle.
 
Q. 21 Draw ΔABC with BC = 6 cm, AB = 5 cm and ∠ABC = 450 . Construct ΔA'B'C similar to ΔABC whose sides are 1*1/2 times the corresponding sides of the ΔABC.
 
1. Construct a DABC in which ÐB=120°, BA= 4cm and BC=5 cm. Construct another DAB’C’similar to DABC such that AB’= AB = 5/4
 
2. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 45°.
 
3. Construct a DABC in which AB = 4.8 cm, BC = 6 cm and AC = 5.5 cm. Draw another triangle whose sides are 1 ½ times the corresponding sides of the given triangle.

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Advanced HOTS Questions with Solutions: Class 10 Mathematics Chapter 11 Constructions

About Chapter 11 Constructions HOTS for Class 10 Mathematics

Strengthen your preparation for Class 10 Mathematics examinations with specialized Chapter 11 Constructions HOTS worksheets. These structured problems are curated to match official CBSE guidelines and help tackle difficult board-level questions.

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FAQs

Where can I download the latest PDF for CBSE Class 10 Mathematics HOTs Constructions?

You can download the teacher-verified PDF for CBSE Class 10 Mathematics HOTs Constructions 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 Mathematics HOTs Constructions 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 Mathematics HOTs Constructions differ from regular textbook questions?

Unlike direct questions that test memory, CBSE Class 10 Mathematics HOTs Constructions 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 Mathematics HOTs Constructions 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 Mathematics HOTs Constructions. These solutions highlight the analytical reasoning and logical steps to help students prepare as per CBSE marking scheme.