# A trigo equation

Geometry Level 3

$\cos^{-1} \frac{41}{A} = 2\sin^{-1} \frac{3}{10}$

Find the value of $$A$$ satisfying the above equation.

Hint: you may consider the angle of a sector $$OPQ$$, where the center of the circle is $$O$$ with radius 10 and chord $$PQ=6$$.

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