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MathNet 2008-part-01 — 165 problems (EN–VI) Question 154

Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)

Question 154

Given is a regular pentagon $ABCDE$. Determine the least value of the expression
$$
\frac{PA + PB}{PC + PD + PE}
$$
where $P$ is an arbitrary point lying in the plane of the pentagon $ABCDE$.