Which of the following segments is a diameter of
O?

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.
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