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Locus of Points (Posted on 2007-12-12) Difficulty: 4 of 5
Let X1, X2, ... , Xn be n≥2 distinct points on a circle C with center O and radius r. What is the locus of points P inside C such that

   ∑ni=1 |XiP|/|PYi| = n

,where the line XiP also intersects C at point Yi.

See The Solution Submitted by Bractals    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: three points again -- that second one got cut off | Comment 7 of 16 |
(In reply to three points again by Charlie)

                                          ------- -------                                           
                                      ---                   ---                                     
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                                -                                   -                               
                              -                                       -                             
                            -                                           -                           
                          -                                               -                         
                        -                                                   -                       
                                                                                                    
                     -                                                         -                    
                                                                                                    
                       ***                                                 ***                      
                 - ************                                        *********** -                
                -****************                                   ****************-               
               -*******************                               *******************-              
              -*********************                             *********************-             
             -************************                         ************************-            
            -**************************                       **************************-           
             ***************************                     ***************************            
            ******************************                  *****************************           
            *******************************               *******************************           
         -  ********************************             ********************************  -        
            **********************************         **********************************           
           **************************************   **************************************          
       -   *******************************************************************************   -      
           *******************************************************************************          
      -     *****************************************************************************     -     
            *****************************************************************************           
     -      *****************************************************************************      -    
            *****************************************************************************           
    -        ***************************************************************************        -   
             ***************************************************************************            
   -          *************************************************************************          -  
              *************************************************************************             
               ***********************************************************************              
  -             *********************************************************************             - 
                 *******************************************************************                
                  *****************************************************************                 
 -                 ***************************************************************                 -
 -                  ************************************************************                   -
 -                   *********************************************************                     -
                       *****************************************************                        
                        **************************************************                          
-                         ********************************************                              -
-                           ***************************************                                 -
-                            *********************************                                      -
-                              ******************...*******                                         -
-                                **************..***..**                                            -
-                                  ************.*****.                                              -
-                                    *********.*****  .                                             -
-                                      *******.****   .                                             -
-                                        *****.**     .                                             -
-                                          ****.     .                                              -
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  -                                  *************                                                - 
                                    ***************                                                 
                                   ****************                                                 
   -                              ******************                                             -  
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     -                         ***********************                                         -    
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      -                       ************************                                        -     
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                             **************************                                             
                             **************************                                             
         -                  ***************************                                    -        
                            ***************************                                             
                            ***************************                                             
                            ***************************                                             
            -               ***************************                                 -           
             -              ***************************                                -            
              -             ***************************                               -             
               -            ***************************                              -              
                -           ***************************                             -               
                 -          **************************                             -                
                            **************************                                              
                             *************************                                              
                     -       ************************                          -                    
                              **********************                                                
                        -     **********************                        -                       
                          -    ********************                       -                         
                            -   ******************                      -                           
                              -  ****************                     -                             
                                - *************                     -                               
                                   - ********                    -                                  
                                      ---                   ---                                     
                                           ------- -------                                          
                                                                                                    
 

  Posted by Charlie on 2007-12-13 00:19:33
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