# Proportional square

Geometry Level 3

$$ABCD$$ is a square. A point $$G$$ is placed on the side $$BC$$ so that $$\frac{BG}{GC} = \frac{1}{3}$$ and the midpoint of the side $$CD$$ is $$E$$. Segments $$BE$$ and $$AG$$ have a common point $$X$$.

If $$\frac{BX}{BE} = \frac{a}{b}$$ where $$a$$ and $$b$$ are positive coprime integers, Find $$a + b$$.

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