New Year's Countdown Day 11: Undecagon

Geometry Level 4

A regular 11-sided polygon ABCDEFGHIJKABCDEFGHIJK is inscribed in a unit circle, as shown below.

If AB×AC×AD×AE×AF=kAB \times AC \times AD \times AE \times AF = \sqrt{k}

for some positive integer k,k, find the sum of digits of k.k.

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