R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 13 - Constructions

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Chapter 13 - Constructions Exercise Ex. 13A

Question 1

Solution 1

 

  

Question 2

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Solution 2

  

Question 3

Solution 3

  

Question 4

Solution 4

 

  

Question 5

Solution 5

 

  

Question 6

Construct a ∆ABC in which AB = 6 cm, A = 30° and B = 60°. Construct another ∆AB'C' similar to ∆ABC with base AB' = 8 cm.

Solution 6

 

  

Question 7

Solution 7

  

Question 8

Solution 8

BC will be divided in the ratio 3 : 4

Question 9

Solution 9

 

  

Question 10

Solution 10

 

  

Chapter 13 - Constructions Exercise Ex. 13B

Question 1

Draw a circle of radius 3 cm. From a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths of the tangents.

Solution 1

  

Question 2

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

Solution 2

 

  

 

Question 3

Draw a circle of radius 3.5 an. Take two points A and B on one of its extended diameter, each at a distance of 5 cm from its centre. Draw tangents to the circle from each of these points A and B.

Solution 3

  

Question 4

Draw a circle with centre O and radius 4 cm. Draw any diameter AB of this circle. Construct tangents to the circle at each of the two end points of the diameter AB.

Solution 4

  

Question 5

Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents from the point P to the circle.

Solution 5

 

  

Question 6

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.

Solution 6

 

Question 7

Draw a circle of radius 4.2 cm. Draw a pair of tangents to this circle inclined to each other at an angle of 45°.

Solution 7

  

Question 8

Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.

Solution 8

 

  

Question 9

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.

Solution 9

  

Question 10

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

Solution 10

  

Chapter 13 - Constructions Exercise FA

Question 1

Draw a line segment AB of length 5.4 cm. Divide it into six equal parts. Write the steps of construction.

Solution 1

  

Question 2

Draw a line segment AB of length 6.5 cm and divide it in the ratio 4 : 7. Measure each of the two parts.

Solution 2

 

  

Question 3

Solution 3

  

Question 4

Solution 4

 

  

Question 5

Solution 5

  

 

 

 

Question 6

Solution 6

   

Question 7

Draw a circle of radius 4.8 cm. Take a point P on it. Without using the centre of the circle, construct a tangent at the point P. Write the steps of construction.

Solution 7

  

Question 8

Draw a circle of radius 3.5 cm. Draw a pair of tangents to this circle which are inclined to each other at an angle of 60°. Write the steps of construction.

Solution 8

 

  

Question 9

Draw a circle of radius 4 cm. Draw tangent to the circle making an angle of 60° with a line passing through the centre.

Solution 9

  

  

Question 10

Draw two concentric circles of radii 4 cm and 6 cm. Construct a tangent to the smaller circle from a point on the larger circle. Measure the length of this tangent.

Solution 10