Problem:
Points A,B,C,D,E, and F lie, in that order, on AF, dividing it into five segments, each of length 1. Point G is not on line AF. Point H lies on GD, and point J lies on GF. The line segments HC,JE, and AG are parallel. Find HC/JE.
Answer Choices:
A. 5/4
B. 4/3
C. 3/2
D. 5/3
E. 2
Solution:
Since △AGD is similar to △CHD, we have HC/1=AG/3. Also, △AGF is similar to △EJF, so JE/1=AG/5. Hence,
JEHC=AG/5AG/3=35.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions
