Question

find the area of a square that can be inscribed in a circle of radius 8 cm.​

Answer 1

Given radius of the circle = 7 cm

Now when a square is inscribed in a ýcircle the diameter of the circle must be the diagonal of the square.

Let the side of the square be 'a' cm.

Therefore, diagonal of square

$\sqrt{ {a}^{2} + a ^{2} }$

Now, diameter of the circle = 2 ×7 cm = 14 cm

$\sqrt{2} \: a = 14$

$a = \frac{14}{ \sqrt{2} }$

Rationalising the denominator

$\frac{14}{ \sqrt{2} } + \frac{ \sqrt{2} }{ \sqrt{2} }$

$\frac{7}{ \sqrt{2} }$

Now, area of square. ..

${a}^{2}$

$({7 \sqrt{2} )}^{2}$

$98cm^{2}$