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ABCDE- regualar pentagon. Find smallest value of expression

Source: Czech-Polish-Slovak 2008, P5

April 14, 2013
geometry proposedgeometry

Problem Statement

ABCDEABCDE is a regular pentagon. Determine the smallest value of the expression ∣PA∣+∣PB∣∣PC∣+∣PD∣+∣PE∣,\frac{|PA|+|PB|}{|PC|+|PD|+|PE|}, where PP is an arbitrary point lying in the plane of the pentagon ABCDEABCDE.
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