Question

relating lengths of sides of inscribed and central angles
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 be congruent.

Explanation:

1. For the central angle \( \angle AOB \): The sides \( OA \) and \( OB \) are radii of the circle. By the definition of a circle, all radii of a given circle are congruent. So the sides of central angles (which are radii) will always be congruent.
2. For the inscribed angle \( \angle ACB \): The sides \( CA \) and \( CB \) are chords of the circle. Chords of a circle are not necessarily congruent unless the arcs they intercept are congruent. Since \( C \) is a point on the circle (not fixed in a way that makes \( CA = CB \) necessarily), the sides of inscribed angles will not always be congruent.

Answer:

First dropdown: always
Second dropdown: not always