Chapter 9.7, Problem 7ST2

To determine

The value of $PF$ from figure.

Answer to Problem 7ST2

The value of $PF=10$

Explanation of Solution

Given information:

It is given $PG=4,PE=15andPH=6$ in 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

  $\begin{array}{c}P{J}^2=PG\times PE\\ =4\times 15\\ =60\end{array}$ …. (1)

Similarly,

  $\begin{array}{c}P{J}^2=PH\times PF\\ =6\times PF\end{array}$ ….. (2)

Now, equating (1) and (2)

  $\begin{array}{l}60=6\times PF\\ PF=10\end{array}$

Therefore, the value of $PF=10$