**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 incenter of a triangle, 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

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**