View source for 1996 OIM Problems/Problem 6

== 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>\lambda _i</math> other than zero, so that

<cmath>(\overline{A_iA_j})^2 = \lambda _i + \lambda _j</cmath>

<cmath>\text{for all } i, j \text{ with } i \ne j\text{.}</cmath>

Show that

a) <math>n \le 4</math>

b) If <math>n=4</math>, then <math>\frac{1}{\lambda _1}+\frac{1}{\lambda _2}+\frac{1}{\lambda _3}+\frac{1}{\lambda _4}=0</math>

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

== Solution ==
{{solution}}

== See also ==
https://www.oma.org.ar/enunciados/ibe11.htm