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 Mango247
Given an acute-angled triangle 
, where
are the midpoints of sides 
respectively. From some point 
inside the triangle, the perpendiculars 
and 
were drawn on sides respectively. It turned out that 
. Prove that H is a point intersection of altitudes of triangle .
, where
are the midpoints of sides 
respectively. From some point 
inside the triangle, the perpendiculars 
and 
were drawn on sides respectively. It turned out that 
. Prove that H is a point intersection of altitudes of triangle .This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 2:15 AM
