**NCERT Solutions for Class 9
Maths Chapter 7 Triangles Ex 7.5**

NCERT Solutions for Class
9 Maths Chapter 7 Triangles Ex 7.5 are the part of NCERT Solutions for Class 9 Maths.
Here you can find the NCERT Solutions for Chapter 7 Triangles Ex 7.5.

**NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.1****NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.2****NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.3****NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.4****NCERT Solutions for Class 9 Maths Chapter 7 Triangles Ex 7.5**

**Ex 7.5 Class 9 Maths Question 1.****
**ABC is a triangle. Locate a point
in the interior of Î”ABC which is equidistant from all the vertices of Î”ABC.

**Solution:**

∴ O is equidistant from two ends B and C of the line segment BC as O lies on the perpendicular bisector of BC.

Similarly, O is equidistant from C and A of the line segment AC as O lies on the perpendicular bisector of AC.

Thus,
the point of intersection O of the perpendicular bisectors of sides BC, CA and
AB is the required point which is equidistant from all the vertices of Î”ABC.

**Ex 7.5 Class 9 Maths Question 2.
**In a triangle locate a point in its interior which
is equidistant from all the sides of the triangle.

**Solution:
**Let BE and CF be the bisectors of ∠ABC and ∠ACB respectively
intersecting AC and AB at E and F respectively.

Since O lies on BE, the bisector of ∠ABC, hence O will be equidistant from AB and BC. Again, O lies on CF, the bisector of ∠ACB. Hence, O will be equidistant from BC and AC. Thus, O will be equidistant from AB, BC and CA.

**Ex 7.5 Class 9 Maths Question 3.
**In a huge park, people are concentrated at three
points (see figure)

A. where there 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 exit.

Where should an ice-cream parlor be set up so that
maximum number of persons can approach it?

[**Hint:** The parlor should be equidistant from A, B and C.]

**Solution:
**The ice-cream parlor should be equidistant from A, B
and C for which the point of intersection of perpendicular bisectors of AB, BC and
CA should be situated.

So, O is the required point which is equidistant from A, B and C.

**Ex 7.5 Class 9 Maths Question 4.
**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?

**Solution:****
**We first divide the hexagon into
six equilateral triangles of side 5 cm as given below:

The number of equilateral triangles of side 1 cm = 1 + 3 + 5 + 7 + 9 = 25

So, the total number of triangles in the hexagon = 6 × 25 = 150.

To find the number of triangles in Fig. (ii), we follow the same procedure.

So, the number of triangles in Fig. (ii) = 12 × 25 = 300

Hence,
Fig. (ii) has more triangles.

**NCERT Solutions for Maths Class 10**