so that the sum of its edges' lengths is minumum.
find, in terms of 
for which there is a set of 
distinct positive integers that has sum greater than 
with 
equilateral. Let 
be the area of the triangle of sides 
,
and 
.
where 
is the circumradius and 
is the volume of the tetrahedron.
,
be the orthocenter of 
.
at 
.
at 
be the midpoint of 
,
meet 
.
at 
.
is tangent to 
where 
.
such that for every 
we have 
.
there exists 
such that![\[u<P(n)-\lfloor P(n)\rfloor <v.\]](http://latex.artofproblemsolving.com/9/4/a/94a8cb1f064e1dea37e8894fb4fd4e34c4c6c845.png)
Generalize the problem!
which moves on line 
towards 
.
.
,
.
satisfying the equation![\[
(f(x+y))^2= f(x^2) + f(2xf(y) + y^2), \quad \forall x, y \in \mathbb{R}.
\]](http://latex.artofproblemsolving.com/2/5/e/25eed911f303ed7cc4e03765a2f943ad4641c451.png)
in the plane of a square 
for which ![\[\max (PA, PC)=\frac1{\sqrt2}(PB+PD).\]](http://latex.artofproblemsolving.com/3/9/8/3984b1970837a85af0bac93fd711843630a1fd99.png)
such that 
and 
for any real numbers 
and 
.
,
at 
.
meets 
.
.
Y by tiendung2006
Dear Mathlinkers,
1. ABC a triangle
2. I the incenter
3. A* the midpoint of AI
4. A'B'C' the I-cevian triangle of ABC
5. A1 the point of intersection of the parallel to BC through A* and B'C'.
6. B1, C1 circularly.
Prouve : A1, B1 and C1 are collinear.
Sincerely
Jean-Louis
1. ABC a triangle
2. I the incenter
3. A* the midpoint of AI
4. A'B'C' the I-cevian triangle of ABC
5. A1 the point of intersection of the parallel to BC through A* and B'C'.
6. B1, C1 circularly.
Prouve : A1, B1 and C1 are collinear.
Sincerely
Jean-Louis
be the cevian triangle of a point 
be the midpoint of 
and let 
be the point of intersection of the parallel to 
.
and 
cyclically.
be the point of intersection of the parallel to 
through 
and the parallel to 
through 
.
and 
cyclically.
and 
concur (at 
)
concur in 
)
are perspective at the point denoted
called cevian quotient of 
o
,
passes through X(667) ( = radical center of the circumcircle, Brocard circle, and the circle with diameter 
)
.
is the centroids of quadrilateral 
.
