[/quote]
,
real numbers 
,
and transform the sequence into 
.
where 
are lengths of parallel sides and 
are other two sides.
?
be a cyclic quadrilateral. Let 
,
be the feet of the perpendiculars from 
,
,
,
if and only if the bisectors of 
and 
are concurrent with 
.
be reals such that 
. Prove that
.
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
is the circumcenter of 
can be inscribed within a circle.
and 
Prove that 
be a triangle. A circle passing through 
intersect at 
and 
intersect at 
.
if and only if 
.
and 
.
be reals such that 
Prove that
Prove that
such that 
.
of positive integers satisfying the following two conditions:
,
is in 
,
and 
;
such that 
is not divisible by 
.
Y by Adventure10
Let 
and 
be two circles with different radii, with the smaller one. The two circles meet at distinct points 
and 
. 
and 
are two points on the circles and , respectively, and such that is the midpoint of 
. 
is extended to meet at 
, while 
is extended to meet at 
. The perpendicular bisector of and the perpendicular bisector of 
meet at 
.
(a) Prove that
.
(b) Prove that
.
and 
be two circles with different radii, with the smaller one. The two circles meet at distinct points 
and 
. 
and 
are two points on the circles and , respectively, and such that is the midpoint of 
. 
is extended to meet at 
, while 
is extended to meet at 
. The perpendicular bisector of and the perpendicular bisector of 
meet at 
.(a) Prove that
.(b) Prove that
.
