Question

In the diagram below, segment PB is a tangent. IF AC = 24 and PA = 3, find PB.

Answer 1

Remember 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.

In this problem, we have that

`PB^2=PC*PA`

where

PC=PA+AC=3+24=27

PA=3

substitute

`\begin{gathered} PB^2=27*3 \\ PB^2=81 \\ PB=9 \end{gathered}`

The answer is option C