is a triangle where 
such that 
and 
,
.
is extended to 
such that 
be an acute triangle with 
,
of side 
,
)
.
and 
,
,
.
intersects line 
at a second point 
.
and 
are perpendicular.
of real numbers such that![\[ a_{m^2 + m + n} = a_{m^2} + a_m + a_n\]](http://latex.artofproblemsolving.com/7/4/4/7447c19e23f40b093bb4cd0cb85a931398570210.png)
for all positive integers 
and 
.
,
and 
.
can be partitioned into several 
Y by
Given an obtuse angle 
, where point 
is different from A. On ray 
, point 
is arbitrarily chosen, also different from 
. Let P be the point of intersection of the tangents to the circumscribed circle of triangle 
drawn at points and . Find the locus of points 
.
, where point 
is different from A. On ray 
, point 
is arbitrarily chosen, also different from 
. Let P be the point of intersection of the tangents to the circumscribed circle of triangle 
drawn at points and . Find the locus of points 
.
.
of the circumcircle 
.
.
.
.
,
.
