Question

classify each part of the circle.

\\(\overline{fg}\\)

\\(b\\)

\\(\angle hag\\)

\\(\overline{fh}\\)

\\(\overline{ah}\\)

\\(\overleftrightarrow{cd}\\)

\\(a\\)

\\(\widehat{fgb}\\)

Explanation:

Identify the geometric elements from the circle diagram

• Center of the circle is point \(A\).
• Points on the circle: \(F, H, B, G\).
• Line \(CD\) is tangent to the circle at point \(B\).
• \(\overline{EG}\) is a chord (where \(E\) is not explicitly labeled but from context of standard circle vocabulary worksheets, \(\overline{FG}\) is a chord, and \(\overline{EG}\) is likely a typo for \(\overline{FG}\) or refers to chord \(\overline{FG}\)). Looking closely at the image, the first item is \(\overline{FG}\), which is a chord.
• \(B\) is a point of tangency.
• \(\angle HAG\) is an angle with its vertex at the center \(A\), so it is a central angle.
• \(\overline{FB}\) is a segment passing through the center \(A\) connecting two points on the circle, so it is a diameter.
• \(\overline{FH}\) is a chord.
• \(\overleftrightarrow{CD}\) is a line that intersects the circle at exactly one point \(B\), so it is a tangent line.
• \(A\) is the center of the circle.
• \(\widehat{FGB}\) is an arc passing through \(F\), \(G\), and \(B\). Since \(\overline{FB}\) is a diameter, \(\widehat{FGB}\) is a semicircle.

Match each given label to its classification

• \(\overline{FG}\): Chord
• \(B\): Point of Tangency
• \(\angle HAG\): Central Angle
• \(\overline{FB}\): Diameter
• \(\overline{FH}\): Chord
• \(\overleftrightarrow{CD}\): Tangent
• \(A\): Center
• \(\widehat{FGB}\): Semicircle

Answer:

Classify each part of the circle:

• \(\overline{FG}\): <blank>Chord</blank>
• \(B\): <blank>Point of Tangency</blank>
• \(\angle HAG\): <blank>Central Angle</blank>
• \(\overline{FB}\): <blank>Diameter</blank>
• \(\overline{FH}\): <blank>Chord</blank>
• \(\overleftrightarrow{CD}\): <blank>Tangent</blank>
• \(A\): <blank>Center</blank>
• \(\widehat{FGB}\): <blank>Semicircle</blank>