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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