and 
Prove that
be the set of real numbers. Find all functions 
where there exist a real constant 
such that 
holds for all reals 
,
,
that satisfy 
.
.
,
.
with integer coefficients such that for any positive integer 
,
is positive and 
Y by Adventure10, Mango247
In a triangle 
let 
be the altitude from 
for 
(
being the foot of the altitude). The circle with diameter meets the two corresponding sides at two points different from 
Denote the length of the segment whose endpoints are these two points by 
Prove that 
let 
be the altitude from 
for 
(
being the foot of the altitude). The circle with diameter meets the two corresponding sides at two points different from 
Denote the length of the segment whose endpoints are these two points by 
Prove that 
intersect 
at 
.
so 
is cyclic. So ![$l_1=XY=\frac{P_2P_3\cdot P_1X}{P_1P_3}=\frac{P_2P_3\cdot P_1Q_1^2}{P_1P_3\cdot P_1P_2}=\frac{(2[P_1P_2P_3])^2}{P_1P_2\cdot P_2P_3\cdot P_3P_1}$](http://latex.artofproblemsolving.com/8/f/c/8fce18afc8b2620393bb9a4f2c4c027c2695d244.png)
.
.
