Question : The length of a side of a square inscribed in a circle is $a\sqrt2$ units. The circumference of the circle is:
Option 1: $2\pi a$ units
Option 2: $\pi a$ units
Option 3: $4\pi a$ units
Option 4: $\frac{2a}{\pi}$ units
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Correct Answer: $2\pi a$ units
Solution :
Given, Side of a square = AB = $\sqrt2 a$ units
We know, the length of the diagonal of a square = $\sqrt2\times$ side
⇒ AC = Diagonal = $\sqrt2 × \sqrt2 a=2a$ units = Diameter of the circle, $d$
$\therefore$ Circumference of circle = $\pi × d$ = $\pi × 2 a$ = $2π a$ units
Hence, the correct answer is $2\pi a$ units.
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