# The immortal kite design!

Geometry Level 4

In the above quadrilateral $$ABCD$$, $$AB=3\text{ m}$$, $$BC=4\text{ m}$$, $$CD=12\text{ m}$$, $$AD=13\text{ m}$$ and angle $$ABC=90^{\circ}$$. If the angle $$BAD$$ is expressible in the form $$\tan^{-1}(-\frac{a}{b})$$, where $$a$$ and $$b$$ are coprime positive integers, find $$b-a$$.

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