Circles

The side of an equilateral triangle is $6\mathrm{cm}$ long. Find the area of the annulus between the incircle and circumcircle of the given triangle. (See the picture.)

A circle of radius $22\mathrm{cm}$ is inscribed into the rhombus $ABCD$. Calculate the measure of the angle $CAB$ if the length of the rhombus side is $90\mathrm{cm}$. (See the picture.) Round the result to two decimal places.

Consider a circle $k$ with radius $2.5\mathrm{cm}$. In the circle is inscribed a convex quadrilateral $ABCD$ so that the diagonal $AC$ is the diameter of the circle, the length of $BC$ is $\sqrt{21}\mathrm{cm}$, and the length of $DC$ is $4\mathrm{cm}$. What is the length of the shortest side of this quadrilateral? (See the picture.)

A regular hexagon $ABCDEF$ is inscribed in a circle with radius of $12\mathrm{cm}$. Calculate the length of its diagonal $EC$. (See the picture.)