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MathNet 2000 — Math Olympiad Vault Question 154

Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault

Question 154

Let $P_1$ be a regular hexagon. Join the midpoints of consecutive sides to form $P_2$, then repeat with $P_2$ to form $P_3$. What is the ratio of the area of $P_3$ to that of $P_1$?

(A) $1/4$
(B) $7/16$
(C) $9/16$
(D) $3/4$
(E) None of the above.