1988 OIM Problems/Problem 3

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Problem

Prove that from all triangles whose vertices are 3, 5 and 7, away from a given point $P$, that the one with the largest perimeter has $P$ as its incenter.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe3.htm