Question

A circle is inscribed inside a square touching all the sides of the square. How many lines of symmetry of the resultant function are present?

Answer 1

Hint: Circle is inscribed touching all sides of the circle means we have a circle inside a square such that it touches all 4 sides of the square.
Line of symmetry is a line that passes from the centre of the image dividing it into two alike parts.
We will draw the figure and count the all possible lines of symmetry one by one and then combine them all to get the final answer.

Complete step-by-step answer:

Circle inscribed (inside) in a square touching it’s all sides can be drawn as:
Now, lines of symmetry are the lines that are imaginary and pass through the centre of an object such that the object is cut into two halves that are alike i.e. mirror image of each other.
Counting the lines of symmetry :
1. Vertical cut:

We can see that it cuts the figure exactly into two halves which are mirror image of each other, thus it is a line of symmetry.
2. Horizontal cut:

We can see that it cuts the figure exactly into two halves which are mirror image of each other, thus it is a line of symmetry.
3. First diagonal cut:

We can see that it cuts the figure exactly into two halves which are mirror image of each other, thus it is a line of symmetry.

4. Second diagonal cut:

We can see that it cuts the figure exactly into two halves which are mirror image of each other, thus it is a line of symmetry.
5. Cut at any random point (passing through the centre):

We can see that the resultant figures are not mirror images of each other.
Similarly all the other random points give the same results.

Therefore, the image has 4 lines of symmetry in total:
Vertical, horizontal and diagonals:

Note: Lines of symmetry are those imaginary lines through which we can imagine the image will be folded and is also called mirror line because the two parts of the figure are exactly alike.
A figure can have any number of lines of symmetry ranging from zero to infinity and the one with zero lines of symmetry is known as an asymmetrical figure.