Question

given the diagram, which represents the radius of circle f?

• \\(\overrightarrow{df}\\)
• \\(\overrightarrow{cb}\\)
• \\(\overrightarrow{hb}\\)
• \\(\overrightarrow{ce}\\)

Explanation:

Identify the center of the circle

The problem asks for the radius of circle \(F\). By definition, the letter naming a circle represents its center point. Therefore, point \(F\) is the center of the circle.

Define a radius

A radius of a circle is a line segment that connects the center of the circle to any point on its outer boundary.

Analyze the given options

We look for a segment that starts at the center \(F\) and ends at a point on the circle's boundary:

• Point \(D\) lies on the circle.
• Point \(F\) is the center.
• Therefore, the segment connecting \(D\) and \(F\), denoted as \(\overline{DF}\), represents a radius of circle \(F\).
• Let's check the other options: \(\overline{CB}\) is a chord, \(\overline{HB}\) is a tangent segment, and \(\overline{CE}\) is a chord.

Match with the choices

The first option is \(\overline{DF}\), which matches our identified radius.

Answer:

• (A) \(\overline{DF}\) (Correct answer)
• (B) \(\overline{CB}\)
• (C) \(\overline{HB}\)
• (D) \(\overline{CE}\)