Question

What is the length of ST? Please explain your answer

Answer 1

We know that

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment. (Intersecting Secant-Tangent Theorem)

so

ST²=RT*QT

RT=7 in

QT=23+7-----> 30 in

ST²=7*30-----> 210

ST=√210-----> 14.49 in

the answer is

RT=14.49 in