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 â–³AGD is similar to â–³CHD, we have HC/1=AG/3. Also, â–³AGF is similar to â–³EJF, 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
