# Ncert Solutions For Class 9 Maths Ex 7.5

## Ncert Solutions For Class 9 Maths Chapter 7 Ex 7.5

Question 1:

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

Solution:

Draw perpendicular bisectors of sides DE,

EF and FD, which meets at O.

Hence, O is the required point.

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:

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$\angle A, \angle B\ and\ \angle C\ of\ \triangle 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.

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?

Solution: