Question

Please help. 10 points. Please do not guess. Guesses will be reported.

Answer 1

The inscribed angle theorem says that

$m\angle CAB=\dfrac12m\angle COB$

Triangle AOC is isosceles because both AO and CO are radii of the circle and have the same length. This means angles CAO and ACO have the same measure and are congruent.

Angles ACO and COD are congruent because they form an alternating interior pair between the parallel lines AC and OD.

Taking all these facts together, we have

$m\angle COB=2m\angle COD$

and since angle COB is made up of angles COD and DOB, these angles must be congruent, and so the arcs they subtend (CD and DB, respectively) must also congruent.