** ***Question 1:*

*Find a point in the interior of △DEF which is at an equal distance or equidistant from all the vertices of △DEF.*

**Solution: **

Draw perpendicular bisectors of sides DE,

EF and FD, which meets at O.

Hence, O is the required point.

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*Question 2:*

*Find a point in the interior of a triangle such that it is at equal distances from all the sides of the triangle.*

** Solution:**

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*Question 3:*

* People are concentrated at three points in a park namely A,B and C. (see Fig.).*

** A: is where swings and slides for children are present**

** B: is where a lake is present**

** C: is where there is a large parking lot and exit**

**Where do you think an ice – cream parlor should be set up such that the maximum number of people can access it? Draw bisectors ∠A,∠B and ∠C of △ABC. Let these angle bisectors meet at O. O is the required point.**

**Solution: **Join AB, BC and CA to get a triangle ABC. Draw the perpendicular bisector of AB and BC. Let them meet at O. Then O is equidistant from A, B and C. Hence, the parlor should be set up at O so that all the other points are equidistant from it.

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*Question 4:*

*Fill the star shaped and hexagonal rangolies [see fig.(i) and (ii)] by filling them with as many equilateral triangles as you can of side 1 cm. What is the number of triangles in both the cases? Which one has the most number of triangles?*

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**Solution:**