In the diagram, $DC$ is a diameter of the large circle centered at $A$, and $AC$ is a diameter of th

Question

In the diagram, $DC$ is a diameter of the large circle centered at $A$, and $AC$ is a diameter of the smaller circle centered at $B$. If $DE$ is tangent to the smaller circle at $F$ and $DC = 12$ then the length of $DE$ is:

Accepted Answer

Sol. [Key Concept: Use the same circle relation as the stem for this option set.]$$\begin{matrix} sin	heta & \ = \frac{r}{3r} = \frac{1}{3} \ DE & \ = 2(2rcos	heta) = 4 	imes 3\left( \frac{2\sqrt{2}}{3} ight) \ DE & \ = 8\sqrt{2} \end{matrix} $$

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