AMC 10 Step by Step
2017 AMC 10BProblem 19P16-20~5 minPrint

Let ABCABC be an equilateral triangle. Extend side AB\overline{AB} beyond BB to a point BB' so that BB=3ABBB'=3 \cdot AB . Similarly, extend side BC\overline{BC} beyond CC to a point CC' so that CC=3BCCC'=3 \cdot BC , and extend side CA\overline{CA} beyond AA to a point AA' so that AA=3CAAA'=3 \cdot CA . What is the ratio of the area of ABC\triangle A'B'C' to the area of ABC\triangle ABC ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.