# Trisectors!

Geometry Level 5

Let $$ABCD$$ be a square. Points $$E, F, G, H$$ are on the line segments $$AB, BC, CD, DA$$ respectively such that $$2AE = EB$$, $$2BF = FC$$, $$2CG = GD$$, and $$2DH = HA$$. The area bounded by the line segments $$AG, BH, CE, DF$$ is a square with side length 1. If $$AB$$ can be written as $$a \sqrt{b}$$, where $$a$$ and $$b$$ are positive integers such that $$b$$ is square-free, find $$a+b$$.

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