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CEMC Gauss (Grade 8), 2000

Geometry Difficulty 2.0 Junior Find the answer Canada

In equilateral triangle $ABC$ , line segments are drawn from a point $P$ to the vertices $A$ , $B$ and $C$ to form three identical triangles. The points $D$ , $E$ and $F$ are the midpoints of the three sides and they are joined as shown in the diagram. What fraction of $\triangle ABC$ is shaded?

(A) $\frac{1}{5}$ (B) $\frac{5}{24}$ (C) $\frac{1}{4}$ (D) $\frac{2}{9}$ (E) $\frac{2}{7}$

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