such that
for all real numbers 
satisfying the equation
?
has circumcenter 
.
and 
intersect at 
,
and 
intersect at 
and 
and 
intersect at 
.
are similar(with vertices in that order), than 
candidates and 
judges, where 
is an odd integer. Each candidate is evaluated by each judge as either pass or fail. Suppose that each pair of judges agrees on at most 
candidates. Prove that ![\[{\frac{k}{m}} \geq {\frac{n-1}{2n}}. \]](http://latex.artofproblemsolving.com/3/8/7/387c8824b28f6422306e3c25b34fccb0a841f4cd.png)
for Girls, PRISMS Online Math Meet for Girls, is happening this spring! 
.
be a polynomial of degree 
such that the polynomial 
divides 
is zero. Prove that 
Y by Mango247
Let 
be a triangle and let 
be a point in its plane, not lying on the circumcircle 
of triangle . Let 
intersect again at points 
, respectively. Let the tangents from 
to the incircle of meet 
at 
and 
, similarly, define 
and 
. Prove that points 
lie on a conic.
by Cosmin Pohoata, Princeton University, USA
be a triangle and let 
be a point in its plane, not lying on the circumcircle 
of triangle . Let 
intersect again at points 
, respectively. Let the tangents from 
to the incircle of meet 
at 
and 
, similarly, define 
and 
. Prove that points 
lie on a conic.by Cosmin Pohoata, Princeton University, USA
is the 
m
are concyclic. If 
are defined similarly, then 
concur, so 
etc are collinear (well-known). Since 
is on the radical axis of 
and 
,
.
to 
,
to 
.
.
