PQ is a radius. QS is tangent to the circle. In this scenario (a radius and a tangent passing through the same point of the radius) the two segments are always perpendicular.
This implies that PQS is a right triangle. We know that PQ = 10 because it's a radius.
Also, we have
[tex] PS=PR+RS = 10+16 = 26 [/tex]
because PR is a radius and RS is given.
So, we can derive QS using the pythagorean theorem:
[tex] QS = \sqrt{PS^2-PQ^2} = \sqrt{676-100} = \sqrt{576} = 24 [/tex]
