#### Chapters

Chapter 2: Polynomials

Chapter 3: Pair of Linear Equations in Two Variables

Chapter 4: Quadratic Equations

Chapter 5: Arithmetic Progression

Chapter 6: Co-Ordinate Geometry

Chapter 7: Triangles

Chapter 8: Circles

Chapter 9: Constructions

Chapter 10: Trigonometric Ratios

Chapter 11: Trigonometric Identities

Chapter 12: Trigonometry

Chapter 13: Areas Related to Circles

Chapter 14: Surface Areas and Volumes

Chapter 15: Statistics

Chapter 16: Probability

## Chapter 9: Constructions

#### RD Sharma solutions for Class 10 Mathematics Chapter 9 Constructions Exercise 9.1 [Page 4]

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

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

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

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

#### RD Sharma solutions for Class 10 Mathematics Chapter 9 Constructions Exercise 9.2 [Pages 9 - 10]

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.

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°.

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

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.

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.

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.

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 5/3^{th} times the corresponding sides of the given triangle.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

#### RD Sharma solutions for Class 10 Mathematics Chapter 9 Constructions Exercise 9.3, 6.3 [Pages 17 - 30]

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.

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.

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.

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.

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

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.

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.

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

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

RD Sharma solutions for Class 10 Mathematics 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 Class 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

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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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