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21

Part of 2016 Purple Comet Problems

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Purple Comet 2016 HS Problem 21

Source:

4/12/2018
On equilateral △ABC\triangle{ABC} point D lies on BC a distance 1 from B, point E lies on AC a distance 1 from C, and point F lies on AB a distance 1 from A. Segments AD, BE, and CF intersect in pairs at points G, H, and J which are the vertices of another equilateral triangle. The area of △ABC\triangle{ABC} is twice the area of △GHJ\triangle{GHJ}. The side length of △ABC\triangle{ABC} can be written r+st\frac{r+\sqrt{s}}{t}, where r, s, and t are relatively prime positive integers. Find r+s+tr + s + t.
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