Question

central angle aob and inscribed angle acb intercept the same arc. concave polygon aobc is formed.
the sides of central angles will dropdown be congruent.
the sides of inscribed angles will dropdown with options always, sometimes, never be congruent.
image of circle with center o, points a, b, c on circumference, segments ao, bo, ac, bc drawn

Explanation:

1. For central angle \( \angle AOB \): The sides of a central angle are radii of the circle (e.g., \( OA \) and \( OB \) are radii of the circle with center \( O \)). By definition, all radii of a circle are congruent. So the sides of central angles will always be congruent.
2. For inscribed angle \( \angle ACB \): The sides of an inscribed angle are chords of the circle (e.g., \( CA \) and \( CB \) are chords). Chords can be congruent in some cases (e.g., if the arcs they subtend are congruent) and not congruent in others. So the sides of inscribed angles will sometimes be congruent.

Answer:

First dropdown: always
Second dropdown: sometimes