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  4. If the diagram, D C is a diameter of the large circle centered at A, and A C is a diameter of the smaller circle centered at B. If D E is tangent to the smaller circle at F and D C=12 then the length of D E is

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Q. If the diagram, $D C$ is a diameter of the large circle centered at $A$, and $A C$ is a diameter of the smaller circle centered at $B$. If $D E$ is tangent to the smaller circle at $F$ and $D C=12$ then the length of $D E$ isMathematics Question Image

Conic Sections

Solution:

$\sin \alpha=\frac{3}{9}=\frac{1}{3}$
also $\sin \alpha=\frac{x}{12}$
(where $E C=x$ )
image
$\frac{1}{3}=\frac{x}{12} \Rightarrow x=4$
$(D E)^{2}=144-16=128$
$ \Rightarrow D E=8 \sqrt{2}$