[/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
.
to 
to 
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
is the circumcenter of 
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 Adventure10
Let 
be the circumcenter and the orthocenter of triangle 
respectively, 
be the midpoint of 
and 
be the intersection point of 
and circumcircle of triangle . Construct triangle if known are points 
and the straight line 
.
(G. Filippovskyy, Kyiv)
be the circumcenter and the orthocenter of triangle 
respectively, 
be the midpoint of 
and 
be the intersection point of 
and circumcircle of triangle . Construct triangle if known are points 
and the straight line 
.(G. Filippovskyy, Kyiv)
This post has been edited 1 time. Last edited by parmenides51, Apr 3, 2024, 7:28 PM
and the Euler line 
with 
.
of 
and mark its center 
and mark its intersection points 
with circle 
