Respuesta :

The diameter of a circle is a segment that connects two points on the circumference and passes through the center.

So, OC, OB and OD are not diameters because O and C don't lie on the circumference.

BD is a diameter, because B and D lie on the circumference, and BD passes through the center.

[tex]\rm \overline{BD}[/tex] is the diameter of the circle O and this can be determined by observing the given diagram.

Given :

A circle whose centre is O.

Check each option to determine which segment is the diameter of circle O.

Option A). [tex]\rm \overline{OC}[/tex]

According to the given diagram [tex]\rm \overline{OC}[/tex] is not the diameter of the circle O.

Option B). [tex]\rm \overline{OD}[/tex]

According to the given diagram [tex]\rm \overline{OD}[/tex] is not the diameter of the circle O it is the radius of the circle O.

Option C). [tex]\rm \overline{BD}[/tex]

According to the given diagram [tex]\rm \overline{BD}[/tex] is the diameter of the circle O.

[tex]\rm \overline{BD}[/tex] = 2 [tex]\rm \overline{OD}[/tex] = 2 [tex]\rm \overline{OB}[/tex]

Option D). [tex]\rm \overline{OB}[/tex]

According to the given diagram [tex]\rm \overline{OB}[/tex] is not the diameter of the circle O it is the radius of the circle O.

For more information, refer to the link given below:

https://brainly.com/question/10712002