Dear Hyacinthists,

I would like to call your attention to the file

http://www.lps.ufrj.br/~sergioln/ime/IMEv9b.pdf
In it you will find lots of proposed and solved problems

from an admissional exam collection year after year.

In particular go to pages 202 e 203 where is presented

in rich details (albeit in portuguese) the solution sent by

Jean-Pierre Ehrmann (merci encore) to a 1986/1987 question.

And to page 209 to another Hyacinthos' members contribution.

Sergio is the author of this huge work and there still is one

unsolved question for which he is asking for help. There it is:

===

Dados dois circulos externos de raios distintos,

mostre que o conjunto de secantes que determinam

em ambos cordas iguais, e' tal que, cada uma dessas

secantes e' tangente a uma parabola, que se pede identificar.

===

Two external circles with different radii are given.

Show that the set of secants that determine in both

circles chords of equal lenghts is such that each of these

secants is tangent to a parabola. The problem asks to

identify the parabola as well.

Last but not least, credits are given at page 3.

Thank you for your attention.

Best regards,

Luis