Refer to the figure below.

Use Thale's Theorem: if A, B, and P are distinct points on a circle where the line AB is a diameter, the angle APB is a right angle.

In △APB;
$AB^2 = AP^2 + PB^2$
$10^2 = (2x)^2 + 6^2$
$2x = 8$
$x = 4$

i.e. AQ = 4cm

Now, In △AQB;
$AB^2 = AQ^2 + QB^2$
$10^2 = (x)^2 + QB^2$
$10^2 = 4^2 + QB^2$
$QB^2 = 84$
$QB = \sqrt{84}$