and a circle 
in the plane. In addition to a normal straightedge, Carl has a special straightedge which, given a line 
and a point 
,
in some order.
![$P \in \mathbb Q[x,y]$](http://latex.artofproblemsolving.com/a/3/8/a384cbf38fd3a7f812b22baaeb0860e7f6eb26c0.png)
with 
and ![$\forall (a,b) \in \mathbb Z^2 \cap [0,d]^2, P(a,b) \in \mathbb Z$](http://latex.artofproblemsolving.com/a/6/5/a65ecb4bb2d9b5e6096f322c2de8bd11b945ed6a.png)
.
?
Y by
Let point 
and 
be on sides 
and 
respectively in 
such that 
. Let 
be the circumcenter of 
and let 
. Prove that 
and 
be on sides 
and 
respectively in 
such that 
. Let 
be the circumcenter of 
and let 
. Prove that 
This post has been edited 1 time. Last edited by Captainscrubz, Apr 11, 2025, 3:51 AM
Reason: resp.
Reason: resp.
be the incenter in 
be the center of spiral similarity that 
a
be the circumcenter of 
is isosceles trapezium
