,
touch sides 
at 
,
lie on the line through 
perpendicular to 
.
be the intersections of 
with 
,
be the projections of 
onto line 
be the second intersections of 
with the incircle 
be the intersection of 
and 
.
bisects segment 
.
be the incentre of 
such that the incircle touches the sides 
meets 
and 
respectively. 
and 
meet the incircle at 
respectively. 
and 
intersect at 
Prove that 
bisects 
then prove 
![$P\in\mathbb{Z}[x]$](http://latex.artofproblemsolving.com/f/3/d/f3d763f4197792a2956273485eb1e94700a43044.png)
has degree 
having 
.
is the leading coefficient of 
Y by
Given an isosceles trapezoid 
. The bisector of angle 
intersects the base 
at point 
. Prove that the center of the circle circumscribed around triangle 
lies on the circle circumscribed around the trapezoid.
(Yu. Blinkov)
. The bisector of angle 
intersects the base 
at point 
. Prove that the center of the circle circumscribed around triangle 
lies on the circle circumscribed around the trapezoid.(Yu. Blinkov)
This post has been edited 1 time. Last edited by parmenides51, Apr 17, 2022, 4:01 PM
be the circumcenter of 
Then 
is cyclic.
