[/quote]
,
,
is the midpoint of 
,
the point of intersection of the tangents at points 
and 
of the circumscribed circle of 
is the midpoint of the segment 
.
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 
,
is the Euler line of triangle 
.
,
,
,
are odd primes and![\[2^ap^b=(p+2)^c-1.\]](http://latex.artofproblemsolving.com/5/8/5/58518a8ebed14836b72af743ff100eae2efba5e2.png)
we have 
.
.
Y by Adventure10, Mango247
Let 
be an orthodiagonal trapezoid such that 
and 
is the larger base. The diagonals intersect at 
, 
is the bisector of 
, 
and 
, 
. Let 
the intersections of the segment 
with 
. Prove that:
(a)
;
(b)
.
Claudiu-Stefan Popa
be an orthodiagonal trapezoid such that 
and 
is the larger base. The diagonals intersect at 
, 
is the bisector of 
, 
and 
, 
. Let 
the intersections of the segment 
with 
. Prove that:(a)
;(b)
.Claudiu-Stefan Popa
considering that 
consequently:
.
and we know that 
so ,
,
analogously 
thus:
