# NCERT solutions for Mathematics Exemplar Class 10 chapter 10 - Construction [Latest edition]

#### Chapters ## Chapter 10: Construction

Exercise 10.1Exercise 10.2Exercise 10.3Exercise 10.4
Exercise 10.1 [Page 114]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 10 Construction Exercise 10.1 [Page 114]

#### Choose the correct alternative:

Exercise 10.1 | Q 1 | Page 114

To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is ______.

• 8

• 10

• 11

• 12

Exercise 10.1 | Q 2 | Page 114

To divide a line segment AB in the ratio 4 : 7, ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3,……… are located at equal distances on the ray AX and the point B is joined to ______.

• A12

• A11

• A10

• A9

Exercise 10.1 | Q 3 | Page 114

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, ....... and B1, B2, B3,....... are located at equal distances on ray AX and BY, respectively. Then the points joined are ______.

• A5 and B6

• A6 and B5

• A4 and B5

• A5 and B4

Exercise 10.1 | Q 4 | Page 114

To construct a triangle similar to a given ΔABC with its sides 3/7 of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, on BX at equal distances and next step is to join ______.

• B10 to C

• B3 to C

• B7 to C

• B4 to C

Exercise 10.1 | Q 5 | Page 114

To construct a triangle similar to a given ΔABC with its sides 8/5 of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. Then minimum number of points to be located at equal distances on ray BX is ______.

• 5

• 8

• 13

• 3

Exercise 10.1 | Q 6 | Page 114

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.

• 135°

• 90°

• 60°

• 120°

Exercise 10.2 [Page 115]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 10 Construction Exercise 10.2 [Page 115]

#### State whether the following statement is True or False:

Exercise 10.2 | Q 1 | Page 115

By geometrical construction, it is possible to divide a line segment in the ratio sqrt(3) : 1/sqrt(3)

• True

• False

Exercise 10.2 | Q 2 | Page 115

To construct a triangle similar to a given ∆ABC with its sides 7/3 of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B1, B2, ...., B7 are located at equal distances on BX, B3 is joined to C and then a line segment B6C' is drawn parallel to B3C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.

• True

• False

Exercise 10.2 | Q 3 | Page 115

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

• True

• False

Exercise 10.2 | Q 4 | Page 115

A pair of tangents can be constructed to a circle inclined at an angle of 170°.

• True

• False

Exercise 10.3 [Page 116]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 10 Construction Exercise 10.3 [Page 116]

Exercise 10.3 | Q 1 | Page 116

Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5

Exercise 10.3 | Q 2 | Page 116

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3. Is the new triangle also a right triangle?

Exercise 10.3 | Q 3 | Page 116

Draw a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct a triangle similar to it and of scale factor 5/3.

Exercise 10.3 | Q 4 | Page 116

Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.

Exercise 10.4 [Pages 117 - 118]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 10 Construction Exercise 10.4 [Pages 117 - 118]

Exercise 10.4 | Q 1 | Page 117

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC. Join P and Q and measure the length PQ.

Exercise 10.4 | Q 2 | Page 117

Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor 4/3. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?

Exercise 10.4 | Q 3 | Page 117

Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.

Exercise 10.4 | Q 4 | Page 117

Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ABC in which PQ = 8 cm. Also justify the construction.

Exercise 10.4 | Q 5 | Page 117

Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Construct a triangle similar to ∆ABC with scale factor 5/7. Justify the construction.

Exercise 10.4 | Q 6 | Page 118

Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Exercise 10.4 | Q 7 | Page 118

Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor 3/2. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.

## Chapter 10: Construction

Exercise 10.1Exercise 10.2Exercise 10.3Exercise 10.4 ## NCERT solutions for Mathematics Exemplar Class 10 chapter 10 - Construction

NCERT solutions for Mathematics Exemplar Class 10 chapter 10 (Construction) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Mathematics Exemplar Class 10 chapter 10 Construction are Division of a Line Segment, Construction of Tangents to a Circle, Constructions Examples and Solutions.

Using NCERT Class 10 solutions Construction exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 10 Construction Class 10 extra questions for Mathematics Exemplar Class 10 and can use Shaalaa.com to keep it handy for your exam preparation