Question

1. which of the following figures shows a major arc?

Explanation:

Step1: Recall major arc definition

A major arc is an arc of a circle that is greater than a semicircle (i.e., its measure is greater than \(180^\circ\)). A semicircle is half of a circle, and a major arc spans more than half the circle.

Step2: Analyze each figure

• First figure: The arc \(TU\) is part of a sector with a central angle (at \(C\)) that looks like an acute angle (less than \(90^\circ\) or at least less than \(180^\circ\)), so the arc is a minor arc (less than semicircle).
• Second figure: The two arcs (from \(A\) and \(B\)): One arc is longer than the other. The longer arc here spans more than half the circle (since the other arc is shorter, so the longer one must be greater than \(180^\circ\)), so this shows a major arc (the longer arc between the two).
• Third figure: This is a full circle, not an arc (a full circle is \(360^\circ\), but an arc is a part; a full circle isn't considered a major arc in the context of "showing a major arc" as it's the whole circle, not a part greater than semicircle but less than full).
• Fourth figure: The arc \(CD\) looks like a minor arc (shorter than a semicircle, as it's a small curve).

Answer:

The second figure (with arcs labeled \(A\) and \(B\), where the longer arc is shown)