# 1500 followers problem! For my friend Xuming!

Geometry Level 5

In $$\Delta ABC$$ , $$m\angle B = 45^\circ$$ , $$m\angle C=54^\circ$$. Point $$O$$ is the circumcenter. Let $$\overline{OE}\perp \overline{AC} \ , \ \overline{OF}\perp \overline{AB}$$ . If the ratio $$\dfrac{OE}{OF}$$ can be expressed as $$\dfrac{a}{\sqrt{b-\sqrt{b}}}$$ where $$a,b \in \mathbb{Z}^+$$ and $$b$$ is square free,

Find the value of $$\displaystyle \left \lfloor\frac{1500}{a+b} \right \rfloor$$.

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