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:

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 to the point of tangency \( G \). By the tangent - radius theorem, the radius is perpendicular to the tangent at the point of contact. So, \( \overline{DG} \) is perpendicular to \( \overleftrightarrow{FG} \).

Answer:

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