Problem: triangle area ratio
March 19, 2008 am31 4:01 am
Consider equilateral triangle ABC. Circles with centers A, B, and C and radii 
Now consider the largest equilateral triangle, DEF, that can be inscribed in that gap. What is the ratio of the areas ABC:DEF?
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JD2718 
An associated problem: Draw the angle bisectors of ABC and extend them so that they intersect the circles at points G, H and I. What is the ratio of of the areas GHI:ABC?