be an acute triangle with 
,
of side 
,
)
.
and 
,
,
.
intersects line 
at a second point 
.
and 
are perpendicular.
such that for all positive real numbers 
,![\[x^2[f(x)+f(y)]=(x+y)f(yf(x)).\]](http://latex.artofproblemsolving.com/2/7/c/27c95af9b083a2a2827d428da24a5152fd926473.png)
Determine all sets 
containing 
and having the property that 
is prime, for all distinct 
?
Y by Adventure10, Mango247
A convex quadrilateral intersects a circle at points 
and 
. (Note that for some letter 
, points 
and 
are on one side of the quadrilateral. Also, the points lie in that specific order on the circle.) Prove that if 
, then quadrilateral formed by these four segments is cyclic.
and 
. (Note that for some letter 
, points 
and 
are on one side of the quadrilateral. Also, the points lie in that specific order on the circle.) Prove that if 
, then quadrilateral formed by these four segments is cyclic.
,
,
,
(the four intersections which are internal to the original circle) - but then concluded that what we are supposed to prove is not generally true.
then the quadrilateral formed by the segments 
is cyclic.
and so forth such that the points on the quadrilateral are 
in order.
Similarly, 
Then it suffices to show that 
Because arcs subtended by chords of the same length have equal measure, we find that 
and 
Then it suffices to show that 
but this is clearly true because 
