Question

A circle is enclosed by a square such that the sides of the square are tangents to the circle. If the radius of the circle is �r��, and the length of the square is ��l��, find the relation between r and l.

• A. r = 2l
• B. r = l/2
• C. r = l
• D. r = l/4

Answer 1

The correct option is B

r = l/2

Here we need to find the relation between the side of the square and the radius of the circle.

It is given that the sides of the square are the tangents to the circle.

This means that all the sides of the square touch the circle at four separate points.

We already know that the line connecting the point of contact of parallel tangents pass through the Centre of the circle and the chord thus formed is the diameter of the circle.

This means that, 2r = l $\Rightarrow r=\frac{l}{2}$

Therefore the relation between the radius of the circle and the side of the square is, r = $\frac{l}{2}$.