Inscribed Hexagon

Geometry Level 5

A hexagon inscribed in a circle has three consecutive sides each of length \(3\) and another \(3\) consecutive sides each of length 5. The chord that divides the hexagon into two isosceles trapezoids has length equal to \(\dfrac{m}{n}\). Where \(m\) and \(n\) are relatively prime positive integers. Find \(m+n\).

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