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

The construction for class 10 Maths notes are provided here. 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 segmentÂ 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 âˆ AA5B) at A3 intersecting AB at the 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

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

**Step 2**: Mark 4 consecutive distances(since the denominator of the required ratio is 4) on BXÂ 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 ABÂ atÂ A’. Î”Aâ€²BCâ€² is the required triangle.

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

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## 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 in anÂ **interior region ofÂ the circle**, any line through thatÂ 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 theÂ PO and bisect it. Let M be the midpoint ofÂ PO.

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

**Step 3**:Â Join PQ and PR

**Step 3**:PQ andÂ 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.