# It slants just fine

Geometry Level 3

Square ABCD has sides of length 1. Points E and F are on $$\overline{BC}$$ and $$\overline{CD}$$ , respectively, so that $$\triangle AEF$$ is equilateral. A square with vertex B has sides that are parallel to those of ABCD and a vertex on $$\overline{AE}$$ . The length of a side of this smaller square is $$\dfrac{a-\sqrt{b}}{c}$$ , where $$a,b$$ , and $$c$$ are positive integers and $$b$$ is not divisible by the square of any prime. Find $$a+b+c$$.

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