Difference between revisions of "1996 OIM Problems/Problem 6"
(Created page with "== Problem == There are <math>n</math> different points <math>A_1, \cdots , A_n</math> in the plane and each point <math>A_i</math> has been assigned a real number <math>\lamb...") |
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Latest revision as of 15:16, 13 December 2023
Problem
There are 
different points 
in the plane and each point 
has been assigned a real number 
other than zero, so that
![\[(\overline{A_iA_j})^2 = \lambda _i + \lambda _j\]](http://latex.artofproblemsolving.com/c/b/7/cb7f40e0740c65839e09c4cb0b786df71fe61743.png)
![\[\text{for all } i, j \text{ with } i \ne j\text{.}\]](http://latex.artofproblemsolving.com/e/8/0/e80b7803ef6261e438e4674e971649a0e5461d28.png)
Show that
a) 
b) If 
, then 
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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