Hello there. To solve this question, we'll have to remember some properties about the radius of a circle and the Pythagorean Theorem.
Given the following diagram:
We want to determine the length of the chord AC.
We already know that the length of the segments OA = 5 and OB = 3.
In the diagram, we get
Notice this is a right triangle, therefore we can determine the length of the segment AB by using the Pythagorean Theorem.
We know that
[tex]\overline{AB}^2+\overline{OB}^2=\overline{OA}^2[/tex]
Hence we get that
[tex]\begin{gathered} \overline{AB}^2+3^2=5^2 \\ \\ \overline{AB}^2+9=25 \\ \\ \overline{AB}^2=25-9=16 \\ \\ \overline{AB}=\sqrt{16}=4 \\ \end{gathered}[/tex]
Since OA is the radius of the circle and D is the midpoint of the arc AC, we get that
[tex]\overline{OA}\equiv\overline{OC}[/tex]
Which means that
[tex]\overline{AB}\equiv\overline{BC}[/tex]
Since
[tex]\overline{AC}=\overline{AB}+\overline{BC}[/tex]
We get that
[tex]\overline{AC}=4+4=8[/tex]
This is the final answer and contained in the last option, D. 8;
