Problem
GEO-B1-M03-P006 Find the Second Segment
#6
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D\in AB\), \(E\in AC\), and \(DE\parallel BC\). It is known that \(AD=4\), \(DB=6\), \(AE=5\). Find \(EC\).
First find the ratio \(AD:AB\).
We have \(AB=AD+DB=10\), so \(\frac{AD}{AB}=\frac{4}{10}=\frac{2}{5}\). From \(\triangle ADE\sim\triangle ABC\), we get \(\frac{AE}{AC}=\frac{2}{5}\). Thus \(AC=5\cdot\frac{5}{2}=\frac{25}{2}\). Therefore \(EC=AC-AE=\frac{25}{2}-5=\frac{15}{2}\).
Students often mistakenly use \(AD:DB\) instead of \(AD:AB\).