Correct option is (C) AD/DB = AE/EC
In \(\triangle ABC, DE \parallel BC \)
Then \(\angle ADE=\angle ABC\)
& \(\angle AED=\angle ACB\) (Corresponding angles are equal as DE || BC)
\(\therefore\) \(\triangle ADE\sim\triangle ABC\) (By AA similarity rule)
\(\therefore\) \(\frac{AD}{AB} = \frac{AE}{AC}\) (By properties of similar triangles)
\(\Rightarrow\) \(\frac{AD}{AB-AD} = \frac{AE}{AC-AE}\) \((\because\,If\,\frac ab=\frac cd\Rightarrow \frac{a}{b-a}=\frac{c}{d-c})\)
\(\Rightarrow\) \(\frac{AD}{DB} = \frac{AE}{EC}\)
