Question

which of the following segments is a radius of \\(\odot a\\)?

a. \\(\overline{gp}\\)
b. \\(\overline{rp}\\)
c. \\(\overline{ta}\\)
d. \\(\overline{tr}\\)

Explanation:

Identify the center and points on the circle

The circle is named \(\odot A\), which means its center is point \(A\).
The points on the boundary of the circle are \(G\), \(T\), \(P\), and \(R\).

Apply the definition of a radius

A radius is a line segment connecting the center of the circle to any point on its boundary.
The segments connecting the center \(A\) to the boundary points are \(\overline{AG}\), \(\overline{AP}\), \(\overline{AR}\), and \(\overline{AT}\).

Evaluate the given options

• Option A: \(\overline{GP}\) is a diameter because it passes through the center \(A\) and connects two boundary points.
• Option B: \(\overline{RP}\) is a chord because it connects two boundary points without passing through the center.
• Option C: \(\overline{TA}\) (or \(\overline{AT}\)) connects the center \(A\) to the boundary point \(T\), which is a radius.
• Option D: \(\overline{TR}\) is a chord.

Answer:

• A. \(\overline{GP}\)
• B. \(\overline{RP}\)
• C. \(\overline{TA}\) (Correct answer)
• D. \(\overline{TR}\)