# A geometry problem by Walid Mustafa

Geometry Level 5

In the figure above, $$\triangle ABC$$ has $$\angle A = 45^\circ$$ and $$\angle B = 30^\circ$$. A line $$DE$$ with $$D$$ on $$AB$$ and $$\angle ADE = 60^\circ$$, divides $$\triangle ABC$$ into two pieces of equal area.

What is the ratio of $$\dfrac{AD}{AB}$$?

Note: The figure above may not be accurate, perhaps $$E$$ is on $$CB$$ instead of $$AC$$.