[/quote]
,
such that
and 
Prove that
that is not isosceles at 
,
be its incircle, which is tangent to 
at 
,
and 
intersect the line passing through 
at 
and 
,
and perpendicular to 
intersect 
and 
at 
and 
,
are collinear and that 
are concurrent.
be a prime number. Prove that there exists an integer 
with 
such that neither 
nor 
is divisible by 
.
such that: 
be an odd prime number. Prove that there exist sequence 
Prove that
with 
,
denote the incenter and 
.
intersects the tangent from 
> Show that 
.
![$P \in \mathbb R[x,y]$](http://latex.artofproblemsolving.com/8/a/0/8a0576299e976c51607959fb68c7c742b2a49c6a.png)
with ![$P \not\in \mathbb R[x] \cup \mathbb R[y]$](http://latex.artofproblemsolving.com/a/f/7/af71ba8c643d5bd8a2928fa6714ccd91713bd641.png)
and 
homeomorphismes of 
,
is an homoemorphisme too.
,
and 
are both integers.
be real numbers such that 
Prove that 
Let 
Prove that 
Y by
Circles 
and 
with centers 
and 
respectively intersect at 
and 
. Ray 
meets again at 
, and ray 
meets 
again at 
. The line through parallel to 
intersects and again at 
and 
, respectively. Prove that 
.
and 
with centers 
and 
respectively intersect at 
and 
. Ray 
meets again at 
, and ray 
meets 
again at 
. The line through parallel to 
intersects and again at 
and 
, respectively. Prove that 
.This post has been edited 1 time. Last edited by parmenides51, Aug 26, 2024, 2:43 PM
