[/quote]
,
be a acute, non-isosceles triangle. 
are the midpoints of sides 
,
the circumcircle and Euler circle of 
lies inside triangle 
and 
intersect 
at 
,
is the point such that 
is the midpoint of 
.
are defined similarly.
then 
;
,
.
are created in the same manner. 
is the orthocenter of 
intersect 
at 
resp. Prove that 
and 
.
Equality holds when 
or 
or 
satisfying 
Prove that 
Proposed by Phan Ngoc Chau
and 
Prove that
Where 
Where 
,
be positive integers such that 
.
is a sequence of integers satisfying 
,
,
,
Prove that there exists 
such that 
such that 
.
satisfying:
and 
-
.
,
,
and 
intersect the circumcircle of 
,
and 
respectively. Let 
,
be diameters in the circumcircles of triangles 
and 
respectively.
.
,
.
states are taking mathcounts state and 
territories are taking mathcounts state 
,
national qualifiers each).
perfect square dates this century, 
this year.
Y by
Summary of the problem: The avatars are not consistent
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Steps to reproduce:
1. change your avatar
2.reload a topic you posted in
3. do #2 to a different topic with your post in it
Expected behavior: Avatars are the same
Frequency: 100%
Operating system(s): MacOS
Browser(s), including version: Chrome latest version
Additional information: refreshing does not help, neither does logging out and in
Page URL: idk
Steps to reproduce:
1. change your avatar
2.reload a topic you posted in
3. do #2 to a different topic with your post in it
Expected behavior: Avatars are the same
Frequency: 100%
Operating system(s): MacOS
Browser(s), including version: Chrome latest version
Additional information: refreshing does not help, neither does logging out and in
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