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 .
Solution 1
First we can draw an image.
Since and are parallel, triangles and are similar. Hence, .
Since and are parallel, triangles and are similar. Hence, . Therefore, . The answer is .
Solution 2
As angle F is clearly congruent to itself, we get from AA similarity, ; hence . Similarly, . Thus, .
Solution 3
Assume an arbitrary value of WLOG. and are parallel, so and are similar. So, which means . By the same logic, , so .
See Also
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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