Find the radius of a circle in which an inscribed square has a side of 8 inches?

Solution:

If the sides of an inscribed square is 8 inches, the diameter of the circle is equal to the diagonal of the square.

Let the side of the square be x. Then the diagonal of the square using Pythagoras theorem is

d² = x² + x²

d² = 2x²

d = √(2x²)

As d = 2r, r = d/2

r = ½ √(2x²)

By further calculation

r = √[2x²/4]

r = √[x²/2]

When x = 8

r = √(64/2)

r = √32

r = √(16 × 2)

r = 4√2

So we get

r = 5.66 in.

Therefore, the radius of the circle is 5.66 in.

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Find the radius of a circle in which an inscribed square has a side of 8 inches?

Summary:

The radius of a circle in which an inscribed square has a side of 8 inches is 5.66 in.