**Construction of Incenter of a Triangle :**

In this section, you will learn how to construct incenter of a triangle.

**Key Concept - In****center**

The point of concurrency of the internal angle bisectors of a triangle is called the incenter of the triangle and is denoted by I.

Before we learn how to construct incenter of a triangle, first we have to learn how to construct angle bisector.

So, let us learn how to construct angle bisector.

To construct an angle bisector, you must need the following instruments.

1. Ruler

2. Compass

3. Protractor

The steps for the construction of an angle bisector are.

**Step 1 :**

Construct an angle of given measure at O using protractor.

**Step 2 :**

With ‘O’ as center draw an arc of any radius to cut the rays of the angle at A and B.

**Step 3 :**

With ‘A’ as center draw an arc of radius more than half of AB, in the interior of the given angle.

**Step 4 :**

With ‘B’ as center draw an arc of same radius to cut the previous arc at ‘C’.

**Step 5 :**

Join OC.

OC is the angle bisector of the given angle.

This construction clearly shows how to draw the angle bisector of a given angle with compass and straightedge or ruler. The angle bisector divides the given angle into two equal parts.

For example, if we draw angle bisector for the angle 60°, the angle bisector will divide 60° in to two equal parts and each part will measure 30°.

Now, let us see how to construct incenter of a triangle.

To construct a incenter, we must need the following instruments.

1. Ruler

2. Compass

Let us see, how to construct incenter through the following example.

Construct the incenter of the triangle ABC with AB = 7 cm, ∠B = 50° and BC = 6 cm. And also measure its radius.

**Step 1 :**

Draw triangle ABC with the given measurements.

**Step 2 :**

Construct the angle bisectors of any two angles (A and B) and let them meet at I.

In the above figure, I is the incenter of triangle ABC.

In the above figure, I is the incenter of triangle ABC

After having gone through the stuff given above, we hope that the students would have understood, how to construct incenter of a triangle.

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