The incentre is (one of the triangle’s points of concurrency formed by) the intersection of the triangle’s three angle bisectors.

**Construction of the Incircle of a Triangle**

The incentre
is (one of the triangle’s points of concurrency formed by) the intersection of the
triangle’s three angle bisectors.

The incentre
is the centre of the incircle ; It is usually denoted by *I*; it is the one
point in the triangle whose distances to the sides are equal.

Construct
the incentre of ΔABC* *with *AB* = 6 cm,* *∠*B *=* *65°* *and* AC *= 7* *cm Also draw
the incircle and measure its radius.

*Solution*

**Step 1 **: Draw the ΔABC with *AB* = 6cm, ∠*B* = 65° and *AC *= 7cm

**Step 2** : Construct the angle bisectors of any
two angles (*A* and *B*) and let them meet at *I*.

Then *I*
is the incentre of ΔABC.
Draw perpendicular from *I* to any one of the side (*AB*) to meet *AB
*at* D*.

**Step 3**: With I as centre and** ***ID *as
radius draw the circle. This circle touches all the* *sides of the triangle
internally.

**Step 4**: Measure inradius

In radius
= 1.9 cm.

Tags : Example Solved Problems | Practical Geometry , 9th Maths : UNIT 4 : Geometry

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9th Maths : UNIT 4 : Geometry : Construction of the Incircle of a Triangle | Example Solved Problems | Practical Geometry

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