Question

central angle aob and inscribed angle acb intercept the same arc. concave polygon aobc is formed. the sides of central angles will be congruent. the sides of inscribed angles will be congruent. always sometimes never

Explanation:

Step1: Recall central - angle property

A central angle has its vertex at the center of a circle. The sides of a central angle are radii of the circle. Since all radii of a circle are congruent, the sides of central angles will always be congruent.

Step2: Recall inscribed - angle property

An inscribed angle has its vertex on the circle. The sides of an inscribed angle are chords (or parts of chords) of the circle. Chords of a circle can have different lengths. So, the sides of inscribed angles will sometimes be congruent (for example, when the inscribed angle is part of an isosceles triangle formed by equal - length chords).

Answer:

The sides of central angles will always be congruent.
The sides of inscribed angles will sometimes be congruent.