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Answer :

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 \(\triangle \)ABC, 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 \(\triangle \)ABC.

- ABC is a triangle. Locate a point in the interior of \(\triangle \) ABC which is equidistant from all the vertices of \(\triangle \)ABC.
- In a huge park, people are concentrated at three points (see figure) A: where these are different slides and swings for children. B: near which a man-made lake is situated. C: which is near to a large parking and exist. Where should an ice-cream parlor be set? up so that maximum number of persons can approach it? [Hint The parlour should be equidistant from A, B and C.]
- Complete the hexagonal and star shaped Rangolies [see Fig. (i) and (ii)] by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

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