with![\[2x^3zf(z)+yf(y) \ge 3yz^2f(x)\]](http://latex.artofproblemsolving.com/a/b/f/abf10d7e679f6f04db556424a0a0eda26f371fd4.png)
for all 
.
,
,
on 
,
,
be the touch points of the incircle of 
.
intersects 
at 
,
.
intersect again at 
. If 
is the tangent point of the 
−
be a function taking in positive integers and outputting nonnegative integers, defined as follows:
is the number of positive integers 
with 
such that the equation 
has an integer solution 
.
such tha
Adit Aggarwal, India.
Y by Adventure10, Mango247
A circle
with radius 
and center 
, and a line 
are drawn on a plane,
such that the distance of from is greater than . Two points 
and
vary on so that the circle with diameter 
is tangent to . Prove
that there is a point
in the plane from which all the segments are
visible at a constant angle.
with radius 
and center 
, and a line 
are drawn on a plane,such that the distance of
from is greater than . Two points 
and
vary on so that the circle with diameter 
is tangent to . Provethat there is a point
in the plane from which all the segments arevisible at a constant angle.
