MathDB

2013.3

Part of Champions Tournament Seniors - geometry

Problems(1)

\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

9/3/2020
On the base of the ABCABC of the triangular pyramid SABCSABC mark the point MM and through it were drawn lines parallel to the edges SA,SBSA, SB and SCSC, which intersect the side faces at the points A1,B1A1_, B_1 and C1C_1, respectively. Prove that MA1+MB1+MC1≤SA+SB+SC\sqrt{MA_1}+ \sqrt{MB_1}+ \sqrt{MC_1}\le \sqrt{SA+SB+SC}
geometrygeometric inequality3D geometrypyramidChampions Tournament