Chapter 9.7, Problem 8ST2

To determine

The value of $PF$ from figure.

Answer to Problem 8ST2

The value of $PJ=12$

Explanation of Solution

Given information:

It is given $PG=4,PE=15andPH=6$ and the figure,

  

When a secant segment and a tangent segment are drawn to a circle from an external point, then the product of the secant segment and its external segment is equal to the square of the tangent segment.

Therefore from given figure

  $\begin{array}{c}P{J}^2=PH\times PF\\ =PH\times \left(PH+HF\right)\\ =8\times \left(8+10\right)\\ =8\times 18\\ =144\end{array}$

Now, taking square root

  $PJ=12$

Since length is always positive so neglecting the negative sign.