the area of hte square that can be inscribed in a circle of radius 8cm is

A . 64cm²

b . 64 root 2 cm ²

c . 128 cm²

d . 256 cm ²

Question

the area of hte square that can be inscribed in a circle of
radius 8cm is
A 64cm2
b 64 root 2 cm 2
c 128 cm2
d 256 cm 2

Ankush Jain · Accepted Answer

When a square is inscribed in a circle, the diagonal of a square must be equal to the diameter of circle

Now, radius of circle, OA = 8 cm ∴ AC = 2 × radius of circle = 2 × 8 cm = 16 cm (1) we know that diagonal AC of square $\Rightarrow AC = \sqrt{2} \times side of square (2)$ On equating (1) and (2), we get $16 = \sqrt{2} \times side of square$ side of square $= \frac{16}{\sqrt{2}} cm$ Now, area of square = (side of square) × (side of square) $= \frac{16}{\sqrt{2}} \times \frac{16}{\sqrt{2}} {cm}^{2} = \frac{256}{2} {cm}^{2} = 128 {cm}^{2}$

the area of hte square that can be inscribed in a circle of radius 8cm is A . 64cm2 b . 64 root 2 cm 2 c . 128 cm2 d . 256 cm 2

the area of hte square that can be inscribed in a circle of radius 8cm is

A . 64cm²

b . 64 root 2 cm ²

c . 128 cm²

d . 256 cm ²