Question

select the correct answer. segment pq is tangent to the circle at point q. which equation describes the relationship between the tangent and secant line segments? a. \\((pq)^2 = (pr)(pq)\\) b. \\(pq = \frac{1}{2}(pr + ps)\\) c. \\((pq)^2 = (pr)(ps)\\) d. \\((pq)^2 = (pr)(qs)\\)

Explanation:

Step1: Recall tangent-secant theorem

The tangent-secant segment theorem states that if a tangent segment and a secant segment are drawn from a point outside the circle, the square of the length of the tangent segment equals the product of the lengths of the entire secant segment and its external segment.

Step2: Match segments to the theorem

For point $P$ outside the circle: tangent segment is $PQ$, entire secant segment is $PS$, external secant segment is $PR$. Substitute into the theorem.
<Expression>
$(PQ)^2 = (PR)(PS)$
</Expression>

Answer:

C. $(PQ)^2 = (PR)(PS)$