NCERT CBSE Class 10th Mathematics Chapter 11: Constructions

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:51 PM IST

Highlights

NCERT CBSE Class 10th Mathematics Chapter 11: Constructions

The eleventh chapter in Mathematics textbook is 'Constructions'.


Determining a Point Dividing a given Line Segment, Internally in the given Ratio M : N

Let AB be the given line segment of length x cm. We are required to determine a point P dividing it internally in the ratio m : n.

Steps of Construction:

  • Draw a line segment AB = x cm.
  • Make an acute ∠BAX at the end A of AB.
  • Use a compass of any radius and mark off arcs. Take (m + n) points A1, A2, … Am, Am+1, …, Am+n along AX such that AA1 = A1A2 = … = Am+n-1 , Am+n
  • Join Am+nB.
  • Passing through Am, draw a line AmP || Am+nB to intersect AB at P. The point P so obtained is the A required point which divides AB internally in the ratio m : n.
    Constructions Class 10 Notes Maths Chapter 11 1
 

Construction of a Tangent at a Point on a Circle to the Circle when its Centre is Known

Steps of Construction:

  • Draw a circle with centre O of the given radius.
    Constructions Class 10 Notes Maths Chapter 11 2
  • Take a given point P on the circle.
  • Join OP.
    Constructions Class 10 Notes Maths Chapter 11 3
  • Construct ∠OPT = 90°.
    Constructions Class 10 Notes Maths Chapter 11 4
  • Produce TP to T’ to get TPT’ as the required tangent.
    Constructions Class 10 Notes Maths Chapter 11 5

The topics discussed in this chapter are as follows:

  • Dividing a Line Segment
  • Constructing Similar Triangles
  • Drawing Tangents to a Circle
  • Number of tangents to a circle from a given point
  • Drawing tangents to a circle from a point outside the circle
  • Drawing tangents to a circle from a point on the circle

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Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3 : 4.

Important Questions for Class 10 Maths Chapter 11 Constructions 1
Hence, PA : PB = 3 : 4

Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Then construct a triangle whose sides are 5/7 times the corresponding sides of ∆ABC

In ∆ABC
AB = 5 cm
BC = 6 cm
∠ABC = 60°
Important Questions for Class 10 Maths Chapter 11 Constructions 3
Hence, ∆A’BC’ is the required ∆.

Construct a triangle with sides 5 cm, 5.5 cm and 6.5 cm. Now construct another triangle, whose sides are 3/5 times the corresponding sides of the given triangle.

Important Questions for Class 10 Maths Chapter 11 Constructions 4
∴ ∆AB’C’ is the required ∆.

Draw a triangle PQR such that PQ = 5 cm, ∠P = 120° and PR = 6 cm. Construct another triangle whose sides are 3/4 times the corresponding sides of ∆PQR.

In ∆PQR,
PQ = 5 cm, PR = 6 cm, ∠P = 120°
Important Questions for Class 10 Maths Chapter 11 Constructions 6
∴ ∆POʻR’ is the required ∆.

Construct a triangle with sides 5 cm, 4 cm and 6 cm. Then construct another triangle whose sides are 2/3 times the corresponding sides of first triangle.

Important Questions for Class 10 Maths Chapter 11 Constructions 8

Steps of Construction:

  • Draw ∆ABC with AC = 6 cm, AB = 5 cm, BC = 4 cm.
  • Draw ray AX making an acute angle with AÇ.
  • Locate 3 equal points A1, A2, A3 on AX.
  • Join CA3.
  • Join A2C’ || CA3.
  • From point C’ draw B’C’ || BC.

∴ ∆AB’C’ is the required triangle.

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