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Max of abcd

Source: China TST 2004 Quiz

February 1, 2009
geometry unsolvedgeometry

Problem Statement

In convex quadrilateral ABCD ABCD, AB\equal{}a, BC\equal{}b, CD\equal{}c, DA\equal{}d, AC\equal{}e, BD\equal{}f. If \max \{a,b,c,d,e,f \}\equal{}1, then find the maximum value of abcd abcd.