A square with a side of 4 cm is inscribed in a circle, find the radius of the circle.
| August 4, 2021 | education
The formula for calculating the radius of a circle circumscribed around a square comes out of the condition of the Pythagorean theorem, since the diameter of a given circle is the diagonal of the square, which divides it into two right triangles, and is the hypotenuse of these triangles:
R = √ (a ^ 2 + a ^ 2) / 2 $
R = √ (4 ^ 2 + 4 ^ 2) / 2 = √ (16 + 16) / 2 = √32 / 2 ≈ 5.66 / 2 = 2.83 cm.
Answer: the radius of the circle is 2.83 cm.
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