Problème1:Let
be the line which connects the tangency points other than in side
of the excircle of convex quadrilateral
.
,
and
are similarly determined by the excircles of
,
and
respectively.
Let
,
,
and
.
Prove that the line
goes through the midpoint of
.
Problème2:Let x, y and z be positive real numbers such that
.
Prove that:
^2}\ge \frac{3}{(xy+yz+zx)^2})
.
Problème3:From three real number
)
we can get another three numbers either
)
or
)
.
Can we get
)
from
)
appliying these two operations adequately many times.
Problème4:Let
be the circumcenter of triangle
.
A line perpendicular to
trough
meets the midperpendicular
at
, and a line perpendicular to
trough
meets the midperpendicular
at
.
If
is the circumcenter of
, prove that
.
Problème5:Find all functions
such that for any
, the equality
+f(y)\big)=2x+f(y))
.
Problème6:Prove that for any
there exists
such that
)
.
Bonne chance.[b]
Accueil 
