Class 10 Maths Notes

# CBSE Class 10 Maths Chapter 11 Constructions  Written by
Constructions Constructions

### Constructions

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 Steps:
• 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 Steps:
• 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.
Steps:
• 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.
Steps:
• 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  