If a square is inscribed in …

If a square is inscribed in a circle, then the diagonals of the square are diameters of the circle.
Let the diagonal of the square be d cm.
Thus, we have:
Radius, r = <nobr>d/2</nobr><amp-mathml data-formula="\[\frac{d}{2}\]" inline="" layout="container"></amp-mathml> cm
Area of the circle = <nobr>πr²</nobr><amp-mathml data-formula="\[\pi r^{2}\]" inline="" layout="container"></amp-mathml> = <nobr>π(d²/4)cm²</nobr>
We know:
d = <nobr>2× √  Side</nobr><amp-mathml data-formula="\[\sqrt{2} \times Side\]" inline="" layout="container"></amp-mathml>

<nobr>⇒Side=d/√2 cm</nobr>
Area of the square = <nobr>(Side)²</nobr>

<nobr>=(d/√2)²</nobr><amp-mathml data-formula="\[= \left ( \frac{d}{\sqrt{2}} \right ) ^{2}\]" inline="" layout="container"></amp-mathml>

<nobr>=(d²/2)cm²</nobr>
Ratio of the area of the circle to that of the square :

<nobr>=πd²/4 / d²/2</nobr><amp-mathml data-formula="\[= \frac{\pi \frac{d^{2}}{4}}{\frac{d^{2}}{2}}\]" inline="" layout="container"></amp-mathml> = <nobr>π/2</nobr>

Thus, the ratio of the area of the circle to that of the square is <nobr>π:2</nobr>