Question

choose the minor arcs on circle a. select all that apply.

\\(\widehat{cb}\\)
\\(\widehat{ed}\\)
\\(\widehat{ef}\\)
\\(\widehat{eb}\\)

Explanation:

Define minor arcs

Using the Arc Measure knowledge point
An arc of a circle is a minor arc if its measure is strictly less than \(180^\circ\) (a semicircle). It is named using its two endpoints.

Identify diameters

We observe the line segments passing through the center \(A\):

• Segment \(E-A-F\) is a straight line, so \(EF\) is a diameter.
• The arc \(\widehat{EF}\) represents a semicircle, which measures exactly \(180^\circ\). Thus, \(\widehat{EF}\) is not a minor arc.

Analyze each option

• \(\widehat{CB}\): The angle \(\angle CAB\) is clearly acute (less than \(90^\circ\)), so the measure of \(\widehat{CB} < 180^\circ\). This is a minor arc.
• \(\widehat{ED}\): The angle \(\angle EAD\) is obtuse but clearly less than \(180^\circ\), so the measure of \(\widehat{ED} < 180^\circ\). This is a minor arc.
• \(\widehat{EF}\): Since \(EF\) is a diameter, the measure of \(\widehat{EF} = 180^\circ\). This is a semicircle, not a minor arc.
• \(\widehat{EB}\): The angle \(\angle EAB\) is obtuse but clearly less than \(180^\circ\), so the measure of \(\widehat{EB} < 180^\circ\). This is a minor arc.

Answer:

• \(\widehat{CB}\) (Correct answer)
• \(\widehat{ED}\) (Correct answer)
• \(\widehat{EF}\)
• \(\widehat{EB}\) (Correct answer)