Maths Notes (Class 10)

CBSE Class 10 Maths Chapter 11 Constructions

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We will study
  • How to divide a line segment in a given ratio
  • Construct a triangle similar to given triangle
  • Construct tangent to a circle
Construction 1To divide a line segment in a given ratio
Let’s divide a line AB in ration 2:3
  • Draw any ray AX, making an acute angle with AB.
  • Locate 5 points A1 to A5 on AX at equal intervals.
  • Join BA5.
  • Through the point A2 , draw a line parallel to BA5 intersecting AB at point C
  • Then, AC : CB = 2 : 3.

Alternate method to divide a line

Let’s divide a line AB in ration 3:2
  • Draw Line AB
  • Draw AX making an acute angle with AB.
  • Draw ray BY parallel to AX
  • Locate points A1, A2, A3 on AX & B1, B2 on BY such that AA1 = A1A2 = A2A3 = BB1 = B1B2.
  • Join A3B2 to meet AB at a point C
Construction 2To construct a triangle similar to a given triangle as per given scale factor.
Given a Δ, construct another triangle whose sides are ¾ of corresponding sides of triangle Δ.
  • Draw Δ
  • Draw ray AX making an acute angle with AB
  • Locate 4 equal points A1 to A4 on AX & Join A4B
  • Draw line through A3 parallel to A4B to intersect AB at B′.
  • Draw line through B′ parallel BC to intersect AC at C’
Construction 3To construct the tangents to a circle from a point outside it.
  • Draw a circle with centre O & Take a point P outside circle.
  • Join PO and bisect it. Let M be the midpoint of PO.
  • Taking M as centre & MO as radius, draw circle. Let it intersect the given circle at Q and R.
  • Join PQ and PR. PQ and PR are required 2 tangents


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