and 
for 
.
.
for which 
is divisible by 
.
is divisible by 
satisfy,
Where 
}
be a fixed square and 
a variable point on segment 
is constructed such that 
is on segment 
and 
is on segment 
.
be the intersection point of lines 
and 
.
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 HWenslawski, ike.chen
Given a triangle 
. Let 
be the circumscribed circle of this triangle, and 
be the inscribed circle of this triangle. Let 
be a circle that touches the sides 
and 
, and also touches the circle internally at point 
. The line 
intersects the circle at two points 
and 
( lies between 
and ). Let 
and 
be the centers of the circles and . Prove that 
.
. Let 
be the circumscribed circle of this triangle, and 
be the inscribed circle of this triangle. Let 
be a circle that touches the sides 
and 
, and also touches the circle internally at point 
. The line 
intersects the circle at two points 
and 
( lies between 
and ). Let 
and 
be the centers of the circles and . Prove that 
.This post has been edited 1 time. Last edited by parmenides51, Sep 3, 2020, 12:56 PM
be the center of 
.
are collinear. But this is obvious after considering the homothety from 
