# In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

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To do:

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Solution:

Let us consider a $\triangle ABC$

We know that,

A point in the interior of the triangle, equidistant from all the sides of the triangle will be its Incenter.

The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle.

Therefore,

In order to locate incentre of  $\triangle ABC$

Let us draw three interior angle bisectors from points $A$, $B$ and $C$.

Let us mark the point of intersection as point $O$.

Therefore, $O$ is the point in its interior which is equidistant from all the sides of the triangle.

Updated on 10-Oct-2022 13:41:30