**In this post, we will discuss Incentre of a triangle which will help you solve geometric questions asked in SSC Exams.**

There are a total of 4 centres of a triangle out of which incentre is the most important centre. One should know all the properties of incentre of a triangle to solve geometric questions in SSC Exams. In our previous posts, we have discussed centroid of a triangle, circumcentre of a triangle, orthocentre of a triangle. In this post, we will discuss Incentre of a triangle which will help you save time in SSC Exams.

###
**What is an Incentre of a Triangle?**

Incentre of a triangle is the point of intersection of the angle bisectors of the interior or exterior angles of the triangle.

### Angle Bisector:

There are two types of angle bisectors.

**1. Interior angle bisector**

**2. Exterior angle bisector**

There are three angles in a triangle, hence there can only be three angle bisectors that can be drawn inside the triangle. The point of intersection of three angle bisectors is called as the incentre of a triangle.

### Properties of Incentre 1:

The angle bisector divides the opposite side of the triangle into a particular ratio. The ratio in which the sides are divided is the ratio of the sides that contains the angle.

Incentre is denoted by the letter 'r.'

In a triangle ABC,

The Exterior angle is equal to the sum of the opposite two angles.

In a triangle ABC,

The angle made by the exterior angle bisectors and the point of intersection is 90° - half the opposite angle.

In the triangle ABC

Hope these Properties of incenter of a triangle have helped you understand the details of incenter of a triangle very well. Do write in the comment section below on how this blog has helped you solve geometric questions asked on Incenter of a triangle in SSC Exams.

To practice questions on incentre of a triangle, download free practice questions.

**AE/EC = AB/BC**

### Properties of Incentre 2:

The incentre 'I' is equidistance from all the three sides. i.e. if a perpendicular is drawn from the centre 'I' to the sides, they will be equal in length.**IE = ID = IF**

### Properties of Incentre 3:

Incentre is the centre of the circle which is inscribed completely inside the triangle. Inradius is the radius from the incentre to the perpendicular drawn on the sides of a triangle.Incentre is denoted by the letter 'r.'

**r = IF = ID = IE**

### Properties of Incentre 4:

The angle made by any side with the incentre is 90° + half the opposite angle.In a triangle ABC,

**∠BIC = 90° + 1/2 ∠A**

**∠AIC = 90° + 1/2 ∠B**

**∠AIB = 90° + 1/2 ∠C**

### Properties of Incentre 5:

For equilateral triangle, r = a/ 2√3 units.### Exterior Angle Bisector

### Properties of Incentre 1:

In a triangle ABC,

Equation (1) All the angles in a triangle equal to 180°

∠A + ∠B + ∠C = 180°

⇒

**∠A + ∠B = 180° - ∠C**
Equation (2) The two Supplementary angles equal to 180°

∠C + ∠C

_{1 }= 180°
⇒

**∠****C**_{1 }= 180° - ∠C
From Equations (1) and (2), we get;

**∠A + ∠B = ∠C**

_{1 }

_{}### Properties of Incentre 2:

The point of intersection of two exterior angle bisectors is represented by the letter "P."The angle made by the exterior angle bisectors and the point of intersection is 90° - half the opposite angle.

In the triangle ABC

**∠BPC = 90° - ∠A/2**

To practice questions on incentre of a triangle, download free practice questions.

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