QUESTION IMAGE
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)\\)
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>
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C. $(PQ)^2 = (PR)(PS)$