Let's go through this problem step by step:

1. Understanding the given information:

   • We have a circle with center $O$.
   • $AB$ and $CD$ are diameters of the circle.
   • The angle $\angle COB$ (formed by diameters $AB$ and $CD$) is given as $50^\circ$.

2. Finding arcs: Since $AB$ and $CD$ are diameters, they split the circle into four arcs.

   • Arc $DB$: This arc corresponds to the angle $\angle COB = 50^\circ$. Therefore, the measure of arc $DB$ is also $50^\circ$.

   • Arc $AD$: This is the arc on the opposite side of arc $DB$ and completes the circle's half. Since $AB$ is a diameter, the semicircle must sum up to $180^\circ$. So, arc $AD = 180^\circ - 50^\circ = 130^\circ$.

   • Arc $AC$: This arc is on the opposite semicircle from $DB$ and has the same measure as arc $DB$. Thus, arc $AC = 50^\circ$.

   • Arc $BC$: Similarly, since $CD$ is a diameter, the opposite arc to $DB$ in the same semicircle must measure the same as arc $AD$. So, arc $BC = 130^\circ$.

3. Summary of answers:

   • Arc $DB = 50^\circ$
   • Arc $AD = 130^\circ$
   • Arc $AC = 50^\circ$
   • Arc $BC = 130^\circ$

Would you like further details or have any questions?

Related Questions

1. How would the arc measures change if $\angle COB$ were different?
2. How do you find the length of an arc if the radius of the circle is given?
3. What is the relationship between central angles and arc measures in a circle?
4. How do inscribed angles relate to their intercepted arcs?
5. What properties do diameters have in terms of dividing a circle into equal arcs?

Tip:

In any circle, the central angle directly determines the measure of the intercepted arc.