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# RD Sharma solutions for Class 10 Mathematics chapter 9 - Constructions

## Chapter 9: Constructions

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 6.30

#### Chapter 9: Constructions Exercise 9.10 solutions [Page 4]

Ex. 9.10 | Q 1 | Page 4

Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.

Ex. 9.10 | Q 1 | Page 4

Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.

Ex. 9.10 | Q 2 | Page 4

Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Ex. 9.10 | Q 2 | Page 4

Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

Ex. 9.10 | Q 3 | Page 4

Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

Ex. 9.10 | Q 3 | Page 4

Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

Ex. 9.10 | Q 4 | Page 4

Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5

Ex. 9.10 | Q 4 | Page 4

Draw a line segment of length 8 cm and divide it internally in the ratio 4 : 5

#### Chapter 9: Constructions Exercise 9.20 solutions [Pages 9 - 10]

Ex. 9.20 | Q 1 | Page 9

Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. Give the justification of the construction.

Ex. 9.20 | Q 1 | Page 9

Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. Give the justification of the construction.

Ex. 9.20 | Q 2 | Page 9

Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th  of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.

Ex. 9.20 | Q 2 | Page 9

Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th  of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.

Ex. 9.20 | Q 3 | Page 9

Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.

Ex. 9.20 | Q 3 | Page 9

Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.

Ex. 9.20 | Q 4 | Page 9

Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)th of the corresponding sides of ΔABC.

Ex. 9.20 | Q 4 | Page 9

Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)th of the corresponding sides of ΔABC.

Ex. 9.20 | Q 5 | Page 9

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. Give the justification of the construction.

Ex. 9.20 | Q 5 | Page 9

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. Give the justification of the construction.

Ex. 9.20 | Q 6 | Page 9

Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)th of the corresponding sides of ΔABC.

Ex. 9.20 | Q 6 | Page 9

Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)th of the corresponding sides of ΔABC.

Ex. 9.20 | Q 7 | Page 9

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3th times the corresponding sides of the given triangle.

Ex. 9.20 | Q 7 | Page 9

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3th times the corresponding sides of the given triangle.

Ex. 9.20 | Q 8 | Page 9

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

Ex. 9.20 | Q 8 | Page 9

Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

Ex. 9.20 | Q 9 | Page 9

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the ∆ABC.

Ex. 9.20 | Q 10 | Page 9

Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.

Ex. 9.20 | Q 10 | Page 9

Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.

Ex. 9.20 | Q 11 | Page 9

Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.

Ex. 9.20 | Q 11 | Page 9

Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.

Ex. 9.20 | Q 12 | Page 9

Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.

Ex. 9.20 | Q 12 | Page 9

Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.

Ex. 9.20 | Q 13 | Page 9

Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are $\frac{3}{5}$ times the corresponding sides of the given triangle.

Ex. 9.20 | Q 14 | Page 9

Construct a triangle PQR with sides QR = 7 cm, PQ = 6 cm and $\angle$PQR = 60º. Then construct another triangle whose sides are $\frac{3}{5}$ of the corresponiding sides of ∆PQR.

Ex. 9.20 | Q 15 | Page 9

Draw a ∆ABC in which base BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of ∆ABC.

Ex. 9.20 | Q 16 | Page 9

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are $\frac{3}{5}$ times the corresponding sides of the given triangle.

Ex. 9.20 | Q 16 | Page 9

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are $\frac{3}{5}$ times the corresponding sides of the given triangle.

Ex. 9.20 | Q 17 | Page 10

Construct a ΔABC in which AB = 5 cm. ∠B = 60° altitude CD = 3cm. Construct a ΔAQR similar to ΔABC such that side ΔAQR is 1.5 times that of the corresponding sides of ΔACB.

Ex. 9.20 | Q 17 | Page 10

Construct a ΔABC in which AB = 5 cm. ∠B = 60° altitude CD = 3cm. Construct a ΔAQR similar to ΔABC such that side ΔAQR is 1.5 times that of the corresponding sides of ΔACB.

#### Chapter 9: Constructions Exercise 9.30, 6.30 solutions [Pages 17 - 30]

Ex. 9.30 | Q 1 | Page 17

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.

Ex. 9.30 | Q 1 | Page 17

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.

Ex. 9.30 | Q 2 | Page 17

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. Give the justification of the construction.

Ex. 9.30 | Q 2 | Page 17

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. Give the justification of the construction.

Ex. 9.30 | Q 3 | Page 17

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Ex. 9.30 | Q 3 | Page 17

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Ex. 9.30 | Q 4 | Page 17

Draw two tangents to a circle of radius 3.5 cm form a point P at a distance of 6.2 cm form its centre.

Ex. 9.30 | Q 4 | Page 17

Draw two tangents to a circle of radius 3.5 cm form a point P at a distance of 6.2 cm form its centre.

Ex. 9.30 | Q 5 | Page 17

Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.

Ex. 9.30 | Q 5 | Page 17

Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45°.

Ex. 9.30 | Q 6 | Page 18

Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.

Ex. 9.30 | Q 6 | Page 18

Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.

Ex. 9.30 | Q 7 | Page 18

Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

Ex. 9.30 | Q 7 | Page 18

Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.

Ex. 6.30 | Q 39 | Page 30

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.

Ex. 6.30 | Q 39 | Page 30

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.

## Chapter 9: Constructions

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 6.30

## RD Sharma solutions for Class 10 Mathematics chapter 9 - Constructions

RD Sharma solutions for Class 10 Maths chapter 9 (Constructions) 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 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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

Concepts covered in Class 10 Mathematics chapter 9 Constructions are To Construct Tangents to a Circle from a Point Outside the Circle., Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given, Construction of Tangent Without Using Centre, Construction of Tangents to a Circle, Construction of Tangent to the Circle from the Point on the Circle, Basic Geometric Constructions, Division of a Line Segment, Division of a Line Segment, Construction of Tangents to a Circle, Constructions Examples and Solutions.

Using RD Sharma Class 10 solutions Constructions 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 RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10 prefer RD Sharma Textbook Solutions to score more in exam.

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