[/quote]
,
,
.
meets the circumcircle 
.
.
:
be reals such that 
and 
Prove that
Where 
Prove that: 
is the sum of 
square numbers
Let 
and 
is the sum of 
is the sum of 
,![\[\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}\geq 4+\frac{8(a-c)^2}{(a+b+c+d)^2}.\]](http://latex.artofproblemsolving.com/7/b/6/7b6e32d32d89ca058a06974e7276f0a5874d90a7.png)
such that 
that satisfy the equation
.
and 
,
and 
be the incenter of triangles 
and 
,
.
,
,
,
are odd primes and![\[2^ap^b=(p+2)^c-1.\]](http://latex.artofproblemsolving.com/5/8/5/58518a8ebed14836b72af743ff100eae2efba5e2.png)
we have 
.
.
Y by
Let 
,
be two circles that intersect at two points 
and 
. Let 
be a point on the segment 
. Consider points 
and 
such that 
and 
lie at , while 
and lie on , and segments 
and 
intersect at . Let 
and 
be the perpendicular bisectors of segments 
and 
. Prove that if , and the line 
concur at point 
, then the line 
is perpendicular on the line 
.
,
be two circles that intersect at two points 
and 
. Let 
be a point on the segment 
. Consider points 
and 
such that 
and 
lie at , while 
and lie on , and segments 
and 
intersect at . Let 
and 
be the perpendicular bisectors of segments 
and 
. Prove that if , and the line 
concur at point 
, then the line 
is perpendicular on the line 
.This post has been edited 3 times. Last edited by parmenides51, Oct 24, 2021, 9:06 AM
