Question

Referring to the figure, find the value of x in circle C.

Answer 1

The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.

Graphically,

`PA\cdot PB=(PD)^2`

In this case, we have:

`3x\cdot5=10^2`

Now, we can solve the equation for x:

`\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ (15x)/(15)=(100)/(15) \\ \text{Simplify} \\ x=(20\cdot5)/(3\cdot5) \\ x=(20)/(3) \\ \text{ or} \\ x\approx6.67 \end{gathered}`

Therefore, the value of x is 20/3 or approximately 6.67.