# Constructions Class 10 Notes: Chapter 11

**CBSE Class 10 Maths Construction Notes:-**Download PDF Here

The construction for class 10 Maths notes are provided here. These notes help for the revision of concepts for the CBSE Class 10 Board Exams 2021-22. In this article, we will discuss how to construct the division of the line segment, constructions of tringles using scale factor, construction of tangents to a circle with two different cases are discussed here in detail. Go through the below article, to learn the construction procedure.

## Dividing a Line Segment

**Bisecting a Line Segment**

**Step 1**: With a radius of more than half the length of the line segment, draw arcs centred at either **end** of the line segment so that they intersect on either **side** of the line segment.

**Step 2**: Join the points of intersection. The line segment is bisected by the line segment joining the points of intersection.

2) Given a line segment AB, divide it in the ratio **m:n**, where both m and n are positive integers.

Suppose we want to divide AB in the ratio 3:2 (m=3, n=2)

**Step 1**: Draw any ray AX, making an acute angle with line segment AB.

**Step 2**: Locate 5 (= m + n) points A1,A2,A3,A4andA5 on AX such that AA1=A1A2=A2A3=A3A4=A4A5

**Step 3**: Join BA5.(A(m+n)=A5)

**Step 4**: Through the point A3(m=3), draw a line parallel to BA5 (by making an angle equal to ∠AA5B) at A3 intersecting AB at point C.

Then, AC : CB = 3 : 2.

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## Constructing Similar Triangles

**Constructing a Similar Triangle with a scale factor**

Suppose we want to construct a triangle whose sides are 3/4 times the corresponding sides of a given triangle

**Steps of Construction:**

**Step 1**: Draw any ray BX making an acute angle with side BC (on the side opposite to the vertex A).

**Step 2**: Mark 4 consecutive distances(since the denominator of the required ratio is 4) on BX as shown.

**Step 3**: Join B4C as shown in the figure.

**Step 4**: Draw a line through B3 parallel to B4C to intersect BC at C’.

**Step 5**: Draw a line through C’ parallel to AC to intersect AB at A’. ΔA′BC′ is the required triangle.

The same procedure can be followed when the scale factor > 1.

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There are two cases while constructing a triangle similar to a given triangle as per the given scale factor. They are:

**Case 1: ** The triangle to be constructed is smaller than the given triangle, and the scale factor is less than 1.

**Case 2:** The triangle to be constructed is larger than the given triangle, and the scale factor is greater than 1.

Here, the scale factor means the ratio of the triangle sides to be constructed with the corresponding sides of the given triangle.

## Drawing Tangents to a Circle

**Tangents: Definition**

A

tangentto a circle is a line whichtouches the circle at exactly one point.

For every point on the circle, there is a unique tangent passing through it.

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### Number of Tangents to a circle from a given point

i) If the point is in an **interior region of the circle**, any line through that point will be a secant. So, in this case, there is no tangent to the circle.

ii) When the point lies on the circle, there is accurately only one tangent to a circle.

iii) When the point lies outside of the circle, there are **exactly two tangents** to a circle.

### Drawing tangents to a circle from a point outside the circle

**To construct the tangents to a circle from a point outside it.**

Consider a circle with centre O and let P be the exterior point from which the tangents to be drawn.

**Step 1**: Join the PO and bisect it. Let M be the midpoint of PO.

**Step 2**: Taking M as the centre and MO(or MP) as radius, draw a circle. Let it intersect the given circle at the points Q and R.

**Step 3**: Join PQ and PR

**Step 3**:PQ and PR are the required tangents to the circle.

### Drawing Tangents to a circle from a point on the circle

To draw a tangent to a circle through a point on it.

**Step 1**: Draw the radius of the circle through the required point.

**Step 2**: Draw a line perpendicular to the radius through this point. This will be tangent to the circle.

#### Watch The Below Video To Understand The Construction of Tangents To The Circle

To learn more about the construction of angles, perpendicular bisectors, similar triangles, and tangents to circles, etc., download BYJU’S – The Learning App today!