Chapter 9.7, Problem 4WE

To determine

To Find: Find the value of x from the given figure.

Answer to Problem 4WE

The value of x is 2

Explanation of Solution

Given information: We have given a figure shown below

  

As we know that when two secants are drawn to a circle from an external point then the product of the one secant segment and its external segment is equal to the product of other secant segment and its external segments.

Therefore, from given figure we must have

  $\begin{array}{c}2x\times \left(x+2x\right)=3\times \left(5+3\right)\\ 2x\times 3x=3\times 8\\ 6x^2=24\\ x^2=\frac{24}{6}\\ x^2=4\\ x=2\end{array}$

Therefore, the value of x is 2