2015 AIME I Problems/Problem 4
Problem
Point lies on line segment with and . Points and lie on the same side of line forming equilateral triangles and . Let be the midpoint of , and be the midpoint of . The area of is . Find .
Solution
Let point A be at (0,0). Then, B is at (16,0), and C is at (20,0). Due to symmetry, it is allowed to assume D and E are in quadrant 1. By equilateral triangle calculations, Point D is at (8,), and Point E is at (18,). By Midpoint Formula, M is at (9,), and N is at (14,). Distance formula shows that BM=BN=MN=. Therefore, by equilateral triangle area formula, x=13, so is 507.
See Also
2015 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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