Question

If a square with side ‘a’ is inserted within a circle such that the corners coincide with the circumference of the circle with diameter ‘d’. Find the relation between ‘a’ and ‘d’.

• A. a = d
• B. a = d/ √2
• C. a = d/2
• D. a = 2d

Answer 1

The correct option is B

a = d/ √2

We are asked to find the relation between the diameter of the circle and the side of the square.

Let us consider the triangle ABC, \(\angle ABC = 90^\circ\)

Therefore we can consider triangle ABC as a right angled triangle with sides = ‘a’, and hypotenuse =‘d’.

Applying the Pythagoras Equation, we get $d^2=a^2+a^2$

$\Rightarrow a^2=\frac{d^2}{\sqrt{2}}$

$\Rightarrow a=\sqrt{\left(\frac{d^2}{2}\right)}$

$\Rightarrow a=\frac{d}{\sqrt{2}}$

Therefore the relation between the sides of the square and the diameter of the circle is, a = $\frac{d}{\sqrt{2}}$