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A Geometric Inequality Involving a Mobile Point in the Place of the Triangle  
 
  Authors: Xiao-Guang Chu, Yu-dong Wu,  
  Keywords: Bottema's inequality, Euler's inequality, Fermat's sum, triangle, mobile point.  
  Date Received: 04/03/2008  
  Date Accepted: 27/08/2009  
  Subject Codes:

Primary 51M16; Secondary 51M25, 52A40.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

By using Bottema's inequality and several identities in triangles, we prove a weighted inequality concerning the distances between a mobile point $ P$ and three vertexes $ A,B,C$ of $ riangle{ABC}$. As an application, a conjecture with regard to Fermat's sum $ PA+PB+PC$ is proved. ;


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