MathDB

\sqrt{MA_1}+ \sqrt{MB_1}+ \sqrt{MC_1}<= \sqrt{SA+SB+SC}, 3d geo ineq

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2013 Seniors p3

September 3, 2020

geometrygeometric inequality3D geometrypyramidChampions Tournament

Problem Statement

On the base of the

ABC

of the triangular pyramid

SABC

mark the point

M

and through it were drawn lines parallel to the edges

SA, SB

and

SC

, which intersect the side faces at the points

A1_, B_1

and

C_1

, respectively. Prove that

\sqrt{MA_1}+ \sqrt{MB_1}+ \sqrt{MC_1}\le \sqrt{SA+SB+SC}