Inequalities
by sqing, Apr 4, 2025, 3:52 AM
Let 
and 
. Prove that
and 
. Prove that
Cyclic inequality
by JK1603JK, Apr 3, 2025, 3:40 PM
Given non-negative real numbers 
satisfying 
Prove that 
Equality holds at 
and its cyclic permutations.
satisfying 
Prove that 
Equality holds at 
and its cyclic permutations.Excalibur Identity
by jjsunpu, Apr 3, 2025, 3:27 PM
Attachments:
This post has been edited 1 time. Last edited by jjsunpu, Today at 12:19 AM
Reason: idk
Reason: idk
Geo Mock #8
by Bluesoul, Apr 1, 2025, 7:05 AM
Consider acute triangle 
. Denote 
as the midpoint of 
, and let 
be a point on segment 
such that 
. Find the length of given 
.
. Denote 
as the midpoint of 
, and let 
be a point on segment 
such that 
. Find the length of given 
.Geo Mock #7
by Bluesoul, Apr 1, 2025, 7:04 AM
Consider 
with 
and 
. Let 
be a point on such that 
. Suppose that the angle bisector of 
is tangent to the circle with diameter 
and say it intersects at point 
. Find the length of 
.
with 
and 
. Let 
be a point on such that 
. Suppose that the angle bisector of 
is tangent to the circle with diameter 
and say it intersects at point 
. Find the length of 
.
then prove 
Ramsey problem: 3 people in 6 pairwise knowing or strangers
by adityaguharoy, Jan 19, 2018, 11:57 AM
Given any collection of 
people. Prove that there is either a collection of 
people among them such that they know each other pairwise, or there is a collection of people among them who are pairwise strangers.
people. Prove that there is either a collection of 
people among them such that they know each other pairwise, or there is a collection of people among them who are pairwise strangers.
.
.
people.
.
is a set of 
is a set of 
.The oldest, shortest words — "yes" and "no" — are those which require the most thought.
April 2021
February 2021
March 2020
February 2018
January 2018
November 2017
September 2017
July 2017
June 2017
May 2017
April 2017
March 2017
February 2017
December 2016
April 2016