The Tiny Triangle

Geometry Level 5

Regular dodecahedron ABCDEFGHIJKLABCDEFGHIJKL with side length 11 is drawn. Segments AFAF, BGBG, and CHCH are then drawn.

The area of the tiny little triangle formed from the intersections of these segments can be expressed as abc\dfrac{\sqrt{a}-b}{c} for positive integers a,b,ca,b,c. Find the value of a+b+ca+b+c.

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