Question 77
Points $A$, $B$, $C$, $D$ lie, in this order, on a circle $\omega$, where $AD$ is a diameter of $\omega$. Furthermore, $AB = BC = a$ and $CD = c$ for some relatively prime positive integers $a$ and $c$. Show that if the diameter $d$ of $\omega$ is also an integer, then $d$ is a perfect square or $2d$ is a perfect square.