1500 followers problem! For my friend Xuming!

Geometry Level 5

In ΔABC\Delta ABC , mB=45m\angle B = 45^\circ , mC=54m\angle C=54^\circ. Point OO is the circumcenter. Let OEAC , OFAB\overline{OE}\perp \overline{AC} \ , \ \overline{OF}\perp \overline{AB} . If the ratio OEOF\dfrac{OE}{OF} can be expressed as abb\dfrac{a}{\sqrt{b-\sqrt{b}}} where a,bZ+a,b \in \mathbb{Z}^+ and bb is square free,

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

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