Question

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

Explanation:

A tangent to a circle and the radius drawn to the point of tangency form a right angle, meaning they are perpendicular. Here, $\overleftrightarrow{FG}$ is tangent to circle $D$ at point $G$, and $\overline{DG}$ is the radius to that point of tangency.

Answer:

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