To answer this question we will use the right triangle altitude theorem.
Using the right triangle altitude theorem we get that:
[tex]BC=\sqrt{DC\times CA}.[/tex]
Substituting BC=16 and CA=23 in the above result we get:
[tex]16=\sqrt{DC\times23}.[/tex]
Therefore:
[tex]256=23DC.[/tex]
Dividing the above result by 23 we get:
[tex]\begin{gathered} \frac{256}{23}=\frac{23DC}{23}, \\ DC=\frac{256}{23}\approx11. \end{gathered}[/tex]
Answer: Option D.
