Question

wx is tangent to ⊙v. what is wx? w 4 in x 5 in v wx = in

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\triangle VWX$ is a right - triangle with $\angle VWX = 90^{\circ}$, $VW$ as the radius of the circle and $VX$ as the distance from the center of the circle to the external point $X$.

Step2: Apply Pythagorean theorem

In right - triangle $\triangle VWX$, by the Pythagorean theorem $VX^{2}=VW^{2}+WX^{2}$. We know that $VW = 4$ in and $VX = 5$ in. Rearranging the formula for $WX$, we get $WX=\sqrt{VX^{2}-VW^{2}}$.

Step3: Substitute values

Substitute $VX = 5$ and $VW = 4$ into the formula: $WX=\sqrt{5^{2}-4^{2}}=\sqrt{25 - 16}=\sqrt{9}=3$ in.

Answer:

3 in