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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