A square with a side of 9√2 is inscribed in a circle. Find the side of a regular triangle circumscribed about this circle.

univerkov | May 20, 2021 | education

Construct the diagonal MP of the square, which will be the diagonal of the square described around it.

The triangle KMP is rectangular, then, by the Pythagorean theorem, MP ^ 2 = 2 * KM ^ 2 = 2 * (9 * √2) ^ 2 = 324.

MP = 18 cm.

Then the radius of the circle is: R = MP / 2 = 18/2 = 9 cm.

The radius of a circle inscribed in an equilateral triangle is:

R = AB * √3 / 6, then AB = 6 * R / √3 = 6 * 9 / √3 = 54 / √3 = 18 * √3 cm.

Answer: The side of the triangle is 18 * √3 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.