Question 30
A hexagon inscribed in a circle has three consecutive sides each of length $3$ and three consecutive sides each of length $5.$ The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length $3$ and the other with three sides each of length $5,$ has length equal to $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$