Chords in Circle and Length Calculation

$AB = 10\text{ cm}$. Since $\angle APB = 90^\circ$, $AP = \sqrt{10^2 - 6^2} = 8\text{ cm}$. Given $AP = 2 AQ \implies AQ = 4\text{ cm}$. In right $\triangle AQB$ (as $\angle AQB = 90^\circ$), $QB = \sqrt{10^2 - 4^2} = \sqrt{84} \approx 9.165 \approx 9.1\text{ cm}$.