Question

in the figure shown, $overleftrightarrow{fg}$ is tangent to circle $d$. what is the relationship between $overline{dg}$ and $overleftrightarrow{fg}$? $\bigcirc$ a. $overline{dg}$ is parallel to $overleftrightarrow{fg}$. $\bigcirc$ b. $overline{dg}$ is perpendicular to $overleftrightarrow{fg}$. $\bigcirc$ c. $overline{dg}$ intersects $overleftrightarrow{fg}$ to form an acute angle. $\bigcirc$ d. $overline{dg}$ intersects $overleftrightarrow{fg}$ to form an obtuse angle.

Explanation:

We know the theorem: A tangent to a circle is perpendicular to the radius at the point of tangency. Here, $\overleftrightarrow{FG}$ is tangent to circle \( D \) at point \( G \), and \( \overline{DG} \) is the radius of the circle at the point of tangency \( G \). So by the tangent - radius theorem, \( \overline{DG} \) is perpendicular to \( \overleftrightarrow{FG} \).

Answer:

B. \(\overline{DG}\) is perpendicular to \(\overleftrightarrow{FG}\)