Question

In the figure, TU is tangent to the circle at point U. Use the figure to answer the question.Suppose RS = 8 in. and ST = 4 in. Find the length of TU to the nearest tenth. Show your work.

Answer 1

Uisng the tangent secant theorem , we have :

$\begin{gathered} x^2\text{ = 4 ( 4 + 8)} \\ x^2\text{ = 4 }\times\text{ 12} \\ x^2\text{ = 48} \\ \text{x =6.9 (nearest tenth)} \\ \text{where x is TU} \end{gathered}$

Hence, TU = 6.9 in