Joining every vertex of a convex pentagon to every other vertex forms three nested figures:

the original outer pentagon
an inner pentagon
a five-pointed star between them

Suppose the perimeters of these three figures are all primes; show that the three primes’ sum is at least 20.

Edited on December 6, 2012, 10:08 pm

Posted by atheron on 2012-12-06 22:07:18