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dividing a convex 5gon by all its diagonals into 10 triangles and 1 smaller 5gon

Source: 2012 Sharygin Geometry Olympiad Final Round 9.7

August 3, 2018

geometrypentagondiagonalsgeometric inequalityconvex

Problem Statement

A convex pentagon

P

is divided by all its diagonals into ten triangles and one smaller pentagon

P'

. Let

N

be the sum of areas of five triangles adjacent to the sides of

P

decreased by the area of

P'

. The same operations are performed with the pentagon

P'

, let

N'

be the similar difference calculated for this pentagon. Prove that

N > N'

.
(A.Belov)