such that ![\[f(f(x)) + xf(xy) = x + f(y)\]](http://latex.artofproblemsolving.com/a/6/f/a6f84dd53eec985b90bad3df6580eeaf29d73195.png)
for all positive real numbers 
and 
.
and 
. Prove that 
. Prove that
Y by Adventure10, Mango247
Dear Mathlinkers,
1. ABC a triangle
2. M the midpoint of BC
3. H the orthocenter of ABC,
4. A'B'C' the orthic triangle of ABC
5. B", C" the midpoints of BB', CC'.
Prove : B", C", A', H et M are concyclic.
Sincerely
Jean-Louis
1. ABC a triangle
2. M the midpoint of BC
3. H the orthocenter of ABC,
4. A'B'C' the orthic triangle of ABC
5. B", C" the midpoints of BB', CC'.
Prove : B", C", A', H et M are concyclic.
Sincerely
Jean-Louis
is midline in 
so 
so 
the circle with diameter MH
we also know that 
hence the conclusion
and 
.
= 
= 
.
are concyclic.... 
)
= 
= 
.
are concyclic.... 
)
