# Ratio of Areas of Trinagles

Geometry Level 1

$$E$$ and $$F$$ are two points on sides $$BC$$ and $$CD$$ of square $$ABCD$$, respectively, and satisfy $$\overline{BE}=\overline{CF}$$. Let $$P$$ be the intersection point of the line segments $$AE$$ and $$BF$$. If the ratio of the areas of triangles $$ABP$$ and $$BEP$$ is $$9:1$$ and $$\angle BAE=\theta$$, what is the value of $$11\sqrt{10} \cos \theta?$$

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