Problem 18

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Problem 18: (2002 AMC 10A 20)

Points $A,B,C,D,E$ and $F$ lie, in that order, on $\overline{AF}$, dividing it into five segments, each of length 1. Point $G$ is not on line $AF$. Point $H$ lies on $\overline{GD}$, and point $J$ lies on $\overline{GF}$. The line segments $\overline{HC}, \overline{JE},$ and $\overline{AG}$ are parallel. Find $HC/JE$.
$\text{(A)}\ 5/4 \qquad$ $ \text{(B)}\ 4/3 \qquad$ $ \text{(C)}\ 3/2 \qquad$ $ \text{(D)}\ 5/3 \qquad$ $ \text{(E)}\ 2$

Solution

Exercise 18: Solution

Points $A,B,C,D,E,F,G,H$ lie, in that order, on $\overline{AH}$, dividing it into seven segments, each of length $1$. Point $K$ is not on line $AH$. Point $L$ lies on $\overline{KD}$, and point $M$ lies on $\overline{KH}$. The line segments $\overline{LC}, \overline{ME},$ and $\overline{AK}$ are parallel. Find $LC/ME$.

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