[/quote]
,
is not a prime number.
and 
be two points in the coordinate plane. A circle is drawn such that 
is a diameter.
be reals such that 
Prove that
be an isosceles triangle with 
,
be its incenter. Incircle touches sides 
at 
,
to 
are 
, respectively. Rays 
intersect 
at 
,
touches incircle at 
.
and 
.
.
and 
intersect at point 
,
is the point on segment 
such that 
.
is isosceles.
-
on the planes 
respectively. Let 
be the intersection point of the line 
and the 
-
.
moves on the perimeter of the circle with center 
, radius 1 on the plane 
,
and 
on the plane 
.
moves on the perimeter of the circle with center 
, radius 1 on the plane 
,
,
,
at 
,
,
intersects lines 
and 
at 
and 
be distinct points on side 
.
be the circumcircle of 
.
.
and 
be positive integers with 
such that 
divides 
.
and 
;
and 
.
wrt 
.
Prove that 
is the angle bisector of 
.
Y by HWenslawski, michaelwenquan, megarnie, AVY2024, Exponent11, PikaPika999, p3nny
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