2002 AMC 10A Problems/Problem 20
Problem
Points and lie, in that order, on , dividing it into five segments, each of length 1. Point is not on line . Point lies on , and point lies on . The line segments and are parallel. Find .
ABCDEFJGH
Solution
Solution $\text{#1}: Since$ (Error compiling LaTeX. ! You can't use `macro parameter character #' in restricted horizontal mode.)AGCHGADHCDCH/AG = CD/AD = 1/3$.
Since$ (Error compiling LaTeX. ! Missing $ inserted.)AGJEGAFJEFEJ/AG = EF/AF = 1/5CH/EJ = (CH/AG)/(EJ/AG) = (1/3)/(1/5) = \boxed{5/3}$. The answer is (D).
Solution \text{#2}: As$ (Error compiling LaTeX. ! Missing $ inserted.)\overline{JE}\overline{AG}\triangle AGF \sim \triangle EJF\frac {AG}{JE} =5\frac {AG}{HC} = 3\frac {HC}{JE} = \boxed{\frac {5}{3}\Rightarrow \text{(D)}}$.
See Also
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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