$\overleftrightarrow{wx}$ is tangent to $\odot v$. what is the radius of the circle?

(image of a circle with center v, point w on the circle, point x outside the circle, segment wx = 3 m, segment xv = 5 m, and segment vw (radius) drawn.)

radius = \boxed{\_} m

Question

$\overleftrightarrow{wx}$ is tangent to $\odot v$. what is the radius of the circle?

(image of a circle with center v, point w on the circle, point x outside the circle, segment wx = 3 m, segment xv = 5 m, and segment vw (radius) drawn.)

radius = \boxed{\_} m

Accepted Answer

# Explanation:
## Step1: Apply the tangent - radius theorem
A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\triangle VWX$ is a right - triangle with $\angle VWX = 90^{\circ}$.
## Step2: Use the Pythagorean theorem
In a right - triangle $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Let the radius $VW = r$, $WX = 3$ m and $VX=5$ m. Then $r^{2}+3^{2}=5^{2}$.
## Step3: Solve for $r$
$$
\begin{align*}
r^{2}+9&=25\
r^{2}&=25 - 9\
r^{2}&=16\
r&=\sqrt{16}\
r& = 4
\end{align*}
$$

# Answer:
$4$

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QUESTION IMAGE

Question

Explanation:

Step1: Apply the tangent - radius theorem

Step2: Use the Pythagorean theorem

Step3: Solve for \(r\)

Answer: