Answer:
AB = 10
Step-by-step explanation:
In circle O, diameter AB is the perpendicular bisector of chord CD at point E. Therefore, given that CD = 8, then CE = ED = 4.
According to the Intersecting Chords Theorem, when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Therefore, in this case:
[tex]\overline{AE} \times \overline{EB}=\overline{CE} \times \overline{ED}[/tex]
Given that EB = 2, and CE = ED = 4, then:
[tex]\overline{AE} \times 2=4 \times 4\\\\\\\overline{AE}=\dfrac{16}{2}\\\\\\\overline{AE}=8[/tex]
To find the diameter AB, sum segments AE and EB:
[tex]\overline{AB}=\overline{AE}+\overline{EB}\\\\\\\overline{AB}=8+2\\\\\\\overline{AB}=10[/tex]
Therefore, the length of the diameter of circle O is 10 units.
