[/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
.
be the feet of the altitudes from 
and 
as the reflections 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 
,
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, Mango247, and 1 other user
Let 
, 
, 
and 
be four points lying on a circle 
(in that order), such that 
is parallel to 
and 
. Let line 
be the tangent to at , and let 
be a point on with 
acute. Prove that 
is trisected by the lines 
and 
; in other words, prove that 
.
S3P1DEC03
, 
, 
and 
be four points lying on a circle 
(in that order), such that 
is parallel to 
and 
. Let line 
be the tangent to at , and let 
be a point on with 
acute. Prove that 
is trisected by the lines 
and 
; in other words, prove that 
.S3P1DEC03
,
