Question

E is an option btw but i need work provided plz!

Answer 1

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

$PS=PR+RS = 10+16 = 26$

because PR is a radius and RS is given.

So, we can derive QS using the pythagorean theorem:

$QS = \sqrt{PS^2-PQ^2} = \sqrt{676-100} = \sqrt{576} = 24$