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 be at . Then, is at , and is at . Due to symmetry, it is allowed to assume and are in quadrant 1. By equilateral triangle calculations, Point is at , and Point is at . By Midpoint Formula, is at , and is at . The distance formula shows that . Therefore, by equilateral triangle area formula, , so is .
See Also
2015 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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