AMC 8 · Geometry

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Points BB, DD, and JJ are midpoints of the sides of right triangle ACGACG. Points KK, EE, II are midpoints of the sides of triangle BJDBJD, etc. If the dividing and shading process is done 100 times (the first three are shown) and AC=CG=6AC = CG = 6, then the total area of the shaded triangles is nearest