# I know the answer not the solution!

Geometry Level pending

A circle with centre $$O$$ is circumscribed about the $$\triangle ABC$$ with $$\angle A$$ as an obtuse angle. The radius $$AO$$ forms an angle $$30$$ with the altitude $$AH$$ on $$BC$$. The extension of angle bisector of $$\angle A$$ meets $$BC$$ at $$F$$ and the circumference of the circle at $$L$$ and the radius $$AO$$ intersects $$BC$$ at point $$E$$. Compute the area of the quadrilateral $$FEOL$$ if it is known that $$AL=4\sqrt{2}$$ $$\text{cm}$$ and $$AH=\sqrt{2\sqrt{3}}$$ $$\text{ cm}$$.

If your answer comes as $$a(b-\sqrt{c})$$ $$\text{ cm}^{2}$$ submit it as $$a+b+c$$.

Note : All angles are in degree.

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