In general, the intersecting secant-tangent theorem states that
Then,
[tex]DC^2=BC*AC[/tex]
Therefore, in our case,
[tex]\begin{gathered} \Rightarrow DC^2=AC*BC=\left(AB+BC\right)*BC=\left(10+15\right)*15 \\ \Rightarrow DC^2=25*15=375 \\ \Rightarrow DC=\sqrt{375}=5\sqrt{15}=19.3649... \end{gathered}[/tex]
The exact answer is DC=5sqrt(15)
