NO-ABEL 2007 Problem 2

The vertices of a convex pentagon $ABCDE$ lie on a circle $\gamma_1$ . The diagonals $AC , CE, EB, BD$ , and $DA$ are tangents to another circle $\gamma_2$ with the same centre as $\gamma_1$ . (a) Show that all angles of the pentagon $ABCDE$ have the same size and that all edges of the pentagon have the same length. (b) What is the ratio of the radii of the circles $\gamma_1$ and $\gamma_2$ ? (The answer should be given in terms of integers, the four basic arithmetic operations and extraction of roots only.)