[Fwd: [EMHL] Inequalities (two questions)]

[Alexandre Tessarollo <tessa@xxxxxxxx>]

    Da outra lista, umas questões interessantes... Alguém se candidata a
provar o que a msg diz ser sabido??

[]'s

Alexandre Tessarollo

PS: Sim, é a lista do Conway...

xpolakis@otenet.gr wrote:

> 1. Let ABC be a triangle, and A'B'C' a triangle inscribed in ABC.
>
> A well-known problem is this:
>
> Prove that the area of A'B'C' is greater or equal of the area of at least
> one of the triangles AB'C', BC'A', CB'A'.
> Prove that the same is true for the perimeters.
>
> Question: Is the same true for the circumradii or inradii of the same
> triangles?
>
> 2. Let ABC be a triangle and A'B'C' the cevian triangle of a point P.
>
> It is known that:
>
> If P = I (ie AA', BB', CC' are the int. angle bisectors)
>
> then 1/AA' + 1/BB' + 1/CC' > 1/BC + 1/CA + 1/AB.
>
> Is the same true for any point P inside ABC?
>
> Antreas
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/