The smallest diagonal of a regular hexagon is 6√3. find the length of the circle around this hexagon

Consider an isosceles triangle formed by a smaller diagonal and two sides of a regular hexagon, the apex angle is 120 °, and the base angle is 30 °. We draw the height in this triangle, denote it by x. And we write in the resulting right-angled triangle the Pythagorean theorem:
x – leg opposite an angle of 30 °;
2x – hypotenuse (hexagon side);
3√3 – second leg (half of the smaller diagonal).
4x² = x² + (3√3) ²
3x² = 27
x² = 9
x = 3
2 * 3 = 6 – side of a regular hexagon and the radius of the circumscribed circle.
C = 2 * π * R = 12π = 37.68.
Answer: the length of the circumscribed circle is 37.68.