Problem
GEO-B2-M04-P001 A Parallel Segment in a Triangle
#1
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D\) and \(E\) lie on sides \(AB\) and \(AC\), and \(DE \parallel BC\). It is known that \(AD:DB=2:3\). Find the ratio \(DE:BC\).
Consider the homothety with centre \(A\) sending \(BC\) to \(DE\).
Since \(AD:DB=2:3\), we have \(AD:AB=2:5\). Because \(DE \parallel BC\), triangles \(ADE\) and \(ABC\) are similar. The similarity ratio is \(\frac{AD}{AB}=\frac{2}{5}\). Therefore \(\frac{DE}{BC}=\frac{2}{5}\), so \(DE:BC=2:5\).
A basic check of understanding the ratio of a homothety.