Question

I've got a couple more questions in my pretest i don't understand any of it

Answer 1

By the Pythagorean Theorem, QS is 7.04. It is well-known that QS=RQ in these circles, so QS+RQ=RS=14.08, which is closest to 14.1.

Answer 2

-- PQS is a right triangle, because a tangent to a circle is
perpendicular to the radius at the point of tangency.

-- You know PQ (a leg) and PS (the hypotenuse) so you can
find the length of the other leg.

QS = (PQ)² - (PS)² = (4.2)² - (8.2)² = 7.043.

-- If you draw the radius PR, then you have another right triangle
back to back with the first one. Each hypotenuse is a radius, so
those are equal, and PQ is common to both triangles.
So RQ is equal to QS.

-- The length of the whole chord RS is double the length of QS .

RS = 2 x (QS) = 2 x (7.043) = 14.085 .

That looks a lot like the third choice down.