#### Question

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

#### Solution

The point which is equidistant from all the sides of a triangle is called the incentre of the triangle. Incentre of a triangle is the intersection point of the angle bisectors of the interior angles of that triangle.

Here, in ΔABC, we can find the incentre of this triangle by drawing the angle bisectors of the interior angles of this triangle. I is the point where these angle bisectors are intersecting each other. Therefore, I is the point equidistant from all the sides of ΔABC.

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Solution In a Triangle Locate a Point in Its Interior Which is Equidistant from All the Sides of the Triangle. Concept: Inequalities in a Triangle.