Problem
GEO-B1-M03-P015 Two Parallels Inside an Angle
#15
★★★☆☆ Level 3 of 5
On the sides of an angle with vertex \(A\), points \(B_1,B_2\) lie on one side and \(C_1,C_2\) on the other, with \(B_1C_1\parallel B_2C_2\). It is known that \(AB_1=6\), \(AB_2=10\), \(AC_2=15\). Find \(AC_1\).
Triangles \(AB_1C_1\) and \(AB_2C_2\) are similar.
From \(B_1C_1\parallel B_2C_2\), \(\triangle AB_1C_1\sim\triangle AB_2C_2\). Thus \(\frac{AB_1}{AB_2}=\frac{AC_1}{AC_2}\). We get \(\frac{6}{10}=\frac{AC_1}{15}\), so \(AC_1=9\).
A clean Thales theorem exercise through triangle similarity.