# 5 Days to 2016 Make it and Bake it

Geometry Level 4

If in a triangle $$ABC$$ an angle bisector is drawn from $$A$$ to $$BC$$ such that it cuts $$BC$$ at $$D$$. If $$\angle BAD = 15^{\circ}$$ and $$\angle ABC =45^{o}$$. If $$AD=5\sqrt{6}$$ and the area of the triangle can be expressed as $$\large{ \frac{m}{\sqrt{n}+p} }$$, for some positive integers $$(m, n, p)$$. Find $$m+n+p$$.

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