5-12-13 and square!

Geometry Level 2

ABCDABCD is a square with AB=13AB=13. Points EE and FF are exterior to ABCDABCD such that BE=DF=5BE=DF=5 and AE=CF=12AE=CF=12.

If the length of EFEF can be represented as ab,a\sqrt b, where aa and bb are positive integers and bb is not divisible by the square of any prime, then find abab.

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