such that for all 
,![\[f(x+yf(x))+y = xy + f(x+y).\]](http://latex.artofproblemsolving.com/c/f/3/cf3d20a041c27244e90876119b4568b7a3e13c03.png)
be a function such that for any real numbers 
satisfying 
,
Given 
,
.
be polygons, no two of which are similar. Show that there are polygons 
where 
is similar to 
so that for no 
does 
.
satisfies 
,
determined by 
in the complex plane.
of 
.
Y by Adventure10
Diagonals of a cyclic quadrilateral 
intersect at point 
. The circumscribed circles of triangles 
and 
intersect at point 
on the side 
. Prove that the point is the center of the inscribed circle of the triangle 
.
intersect at point 
. The circumscribed circles of triangles 
and 
intersect at point 
on the side 
. Prove that the point is the center of the inscribed circle of the triangle 
.This post has been edited 2 times. Last edited by parmenides51, Feb 25, 2024, 7:28 AM
