Chapter 9, Problem 24CR

To determine

To find: the value of x .

Answer to Problem 24CR

The value of x is $\sqrt{55}$ .

Explanation of Solution

Given:

The circle is shown below:

Calculation:

For circle with tangent and secant as shown below:

Tangent-secants theorem states that:

  $T{X}^2=AX\cdot BX$

For given circle,

Hence, according to Tangent-secants theorem:

  $\begin{array}{c}{x}^2=5\left(6+5\right)\\ =5\left(6+5\right)\\ x=\sqrt{55}\left(\text{positive}\text{}\text{value}\text{}\text{is}\text{}\text{considered}\right)\end{array}$

Hence, the value of x is $\sqrt{55}$ .