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TOT 104 1985 Autumn S1 PA+PB+PC+PD <=L+D_1+D_2

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August 26, 2019
convexdiagonalSumperimetergeometric inequality

Problem Statement

We are given a convex quadrilateral and point MM inside it . The perimeter of the quadrilateral has length LL while the lengths of the diagonals are D1D_1 and D2D_2. Prove that the sum of the distances from MM to the vertices of the quadrilateral are not greater than L+D1+D2L + D_1 + D_2 .
(V. Prasolov)
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