[/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 
to the lines 
,
,
,
if and only if the bisectors of 
and 
are concurrent with 
be reals such that 
. Prove that
.
be the feet of the altitudes from 
to 
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
can be inscribed within a circle.
and 
Prove that 
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
Let 
be an isosceles acute-angled triangle and let
and 
be the feet of the altitudes drawn from its vertices 
and 
, respectively. Let 
be the intersection point of the altitudes of the triangle, 
the center of its circumcircle, and 
the midpoint of the side 
. Lines 
and intersect at point 
and lines 
and 
at point 
. Prove that the lines 
and 
are parallel.
be an isosceles acute-angled triangle and let
and 
be the feet of the altitudes drawn from its vertices 
and 
, respectively. Let 
be the intersection point of the altitudes of the triangle, 
the center of its circumcircle, and 
the midpoint of the side 
. Lines 
and intersect at point 
and lines 
and 
at point 
. Prove that the lines 
and 
are parallel.This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 1:59 AM
