Slid sectors

Geometry Level 3

A circle of radius 2020 is sliced into three congruent sectors, which are then slid apart to create a green equilateral triangle with side length 9.9. A larger equilateral triangle is then circumscribed.

The side length of this large triangle can be written as a+bdc\frac{a+b\sqrt{d}}{c} with dd square-free and a,b,ca, b, c irreducible.

What is the value of a+b+c+d?a+b+c+d?

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