Question 5
Rectangle $ABCD$ has dimensions $AB = 107$ and $BC = 16,$ and rectangle $EFGH$ has dimensions $EF = 184$ and $FG = 17.$ Points $D,$ $E,$ $C,$ and $F$ lie on line $DF$ in that order, and $A$ and $H$ lie on opposite sides of line $DF,$ as shown. Points $A,$ $D,$ $H,$ and $G$ lie on a common circle. Find $CE.$
