[/quote]
,
distinct circles in a plane, with radius 
.
circles, which form a set 
,
satisfy:
.
with incentre 
,
and 
by the midpoints of 
and 
respectively, and 
and 
be the feet of the altitudes from 
and 
the line being tangent tot he circumcircle of triangle 
,
the reflection of 
.
by the intersection of 
and 
be the intersection of 
and 
analogously. If 
is the intersection of 
and 
,
.
and 
.
be the point on the line 
.
and 
intersect at point 
,
is the point on segment 
such that 
.
is isosceles.
be a point inside of it such that the square root of the distance of 
be a triangle. On side 
and 
such that 
take points 
and 
such that 
and on side 
take points 
such that 
Let 
and 
are concurrent.
lie the following points: 
and 
on 
,
on 
,
on 
.![\[
P = AM\cap BN,\quad
R = KM\cap LN,\quad
S = KN\cap LM,
\]](http://latex.artofproblemsolving.com/7/e/a/7ea90a0f1261ed7445bbac58fb0cdd76810259f3.png)
and let the line 
meet 
.
,
are collinear.
.
intersects 
and 
and 
,
of triangle 
lies on the circle 
and 
coincide.
be a triangle and 
and 
be two points on 
,
such that 
and let 
.
to the interior angle bisector of 
intersect 
in 
.
.
,
at 
,
to 
, respectively. Rays 
intersect 
at 
,
touches incircle at 
.
and 
are equal.
let 
and 
.
and 
,
.
.
,
,
at points 
be the projection of 
.
intersects the circumcircle of 
.
and 
intersect 
and 
respectively. Prove that the lines 
,
,
are concurrent.
Y by GeoMorocco, Maximilian113, Ciobi_, Victoria_Discalceata1, KhuongTrang, TNKT, PikaPika999
Hi everyone,
As we know, the pqr/uvw method is a powerful and useful tool for proving inequalities. However, transforming an expression
into 
or 
can sometimes be quite complex. That's why I’ve written a program to assist with this process.
I hope you’ll find it helpful!
Download: pqr_convert
Screenshot:
As we know, the pqr/uvw method is a powerful and useful tool for proving inequalities. However, transforming an expression
into 
or 
can sometimes be quite complex. That's why I’ve written a program to assist with this process.I hope you’ll find it helpful!
Download: pqr_convert
Screenshot:
in Mathematica to do this.
conversion as well?
