[/quote]
,
that satisfy the equation 
.
be a circle, and let a line 
intersect 
and 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
have the same incenter 
.
is concyclic iff 
is concurrent
be the nonnegative integers in 
where 
.
.
.
such that 
where 
,
?
where 
,
be a scalene triangle with circumcircle 
and circumcircle 
.
and 
as the midpoints of 
and 
,
to 
.
meets 
,
intersects 
.
at 
and 
at 
.
intersect 
,
intersect 
.
is the reflection of 
and 
lies on the circumcircle of 
.
be real numbers such that 
and 
and determine the equality cases.
be positive real integer such that 
Prove that
such that 
and 
satisfying :![\[n^{2p}=m^2+n^2+p+1\]](http://latex.artofproblemsolving.com/7/4/e/74ee592cb8b3f3a3996ea34f40b78fde9d3672fc.png)
and 
are integers and 
is a prime number.
and 
Prove that
Approach: I'm trying to factor 
to get 
.
such that 
divides 
.
Y by centslordm
Point 
is given on the side of the acute angle. Construct a point 
on this side such that the distance from it to point is equal to the distance from to the other side of the angle.
is given on the side of the acute angle. Construct a point 
on this side such that the distance from it to point is equal to the distance from to the other side of the angle.This post has been edited 4 times. Last edited by parmenides51, Jul 26, 2021, 3:06 PM
Reason: country typo
Reason: country typo
