-- 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.
