1. A circle is circumscribed about an equilateral triangle, and another circle is inscribed in the triangle. What is the ratio of the area of the larger circle to the area of the smaller circle?

2.   A regular hexagon is inscribed in a circle. another regular hexagon is circumscribed about the circle so  that the midpoints of its sides coinside with the vertices of the first hexagon. What is the ratio of the area of the larger hexagon to the area of the smaller?

3. Each side of a regular hexagon is extended by an amount equal to its length, as shown, and the endpoints of these segments are joined to form a larger regular hexagon. What is the ratio of the area of the larger hexagon to the area of the smaller hexagon?

Reference

NCTM. Mathematics Teacher.