A circle is inscribed in a regular quadrangle with a side of 4 cm. find the radius of the circle

univerkov | June 17, 2021 | education

A circle is inscribed in a regular quadrangle with a side of 4 cm. find the radius of the circle; side of a regular triangle circumscribed about a given circle.

Since a circle is inscribed in the square, its radius is equal to half the length of the side of the square.

R = AB / 2 = 4/2 = 2 cm.

Let’s apply the formula for the radius of a circle inscribed in a regular triangle.

R = a * √3 / 6, where a is the side of a regular triangle.

Then a = KM = R * 6 / √3 = 2 * 6 / √3 = 4 * √3 cm.

Answer: The radius of the circle is 2 cm, the side of the triangle is 4 * √3 cm.

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