MathDB

54

Part of 1984 IMO Longlists

Problems(1)

Find necessary and sufficient condition for regular polygon.

Source:

10/13/2010
Let PP be a convex planar polygon with equal angles. Let l1,⋯ ,lnl_1,\cdots, l_n be its sides. Show that a necessary and sufficient condition for PP to be regular is that the sum of the ratios lili+1(i=1,⋯ ,n;ln+1=l1)\frac{l_i}{l_{i+1}} (i = 1,\cdots, n; l_{n+1}= l_1) equals the number of sides.
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