*Problem #13*

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In the figure below, P is the midpoint of BC, Q is the midpoint of AC, R
is the midpoint of AB, X is the midpoint of CP, Y is the midpoint of AQ,
and Z is the midpoint of BR.

Find the ratio of the area of the shaded triangle to the area of triangle
ABC. [Note: Although triangle ABC is equilateral, the ratio is independent
of this fact.]

Can you generalize this?