# 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 \(11\sqrt{10} \cos \theta?\)