# Find the value of $$x$$

Geometry Level 3

$\large \sin 20^\circ \cos 50^\circ = x \sec 10^\circ$ If the real number $$x$$ satisfying the above equation is of the form $$\dfrac {\sqrt {a}}{b}$$, where $$a$$ and $$b$$ are integers, and $$a$$ is square-free, find $$a+b$$.

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