Question

n the diagram below, segment PB is a tangent. IF AC = 45 and PA = 4, find PB.

Answer 1

Given that segment PB is a tangent, you can identify that segment PC is secant.

You know that:

$\begin{gathered} AC=45 \\ PA=4 \end{gathered}$

According to the Intersecting Secant-Tangent Theorem:

$Tangent=\sqrt{Secant\text{ }segment\cdot External\text{ }secant\text{ }segment}$

In this case, you can identify that:

$Secant\text{ }segment=PC=PA+AC=4+45=49$$External\text{ }secant\text{ }segment=PA=4$

Therefore, you can determine that:

$\begin{gathered} PB=\sqrt{49\cdot4} \\ PB=14 \end{gathered}$

Hence, the answer is: Option b.