Question 72
Let $\omega_{1}$ be a circle with diameter $J K$. Let $t$ be the tangent to $\omega_{1}$ at $J$ and let $U \neq J$ be another point on $t$. Let $\omega_{2}$ be the smaller circle with centre $U$ which touches $\omega_{1}$ at a single point $Y$. Let $I$ be the second intersection point of $J K$ with the circumcircle of triangle $J Y U$ and let $F$ be the second intersection point of $K Y$ with $\omega_{2}$. Show that $F U J I$ is a rectangle.
