The perimeter of a regular triangle inscribed in a circle is 45 cm. Find the side of a regular quadrilateral inscribed in the same circle.

Given: regular triangle ABC;
triangle ABC is inscribed in a circle;
P avs = 45 cm;
MНCD a regular quadrilateral is inscribed in the same circle.
Find: length KР -?
Decision:
1) AB = BC = AC = a = 45: 3 = 9 (cm);
2) the radius of the circumscribed circle around a regular triangle is: R = a √3 / 3. Then R = 9 √3 / 3 = 3√3 cm;
3) the radius of the circumscribed circle about a regular quadrangle is: R = a √2 / 2. Then a = √2 R. Substitute instead of R = 3√3 cm and a = KP and we get: KP = √2 R = a = √2 * 3√3 = 3√6 (cm).
Answer: KР = KН = НM = MР = 3√6 cm.