and 
.
Where 
satisfies 
.
,
.
and a constant 
,
and 
are also friendly polynomials. Prove that 
.
lying outside the circle 
,
and 
.
is chosen on the segment 
.
and 
be the midpoints of segments 
and 
respectively. The circumcircle of triangle 
intersects 
)
passes through the centroid of triangle 
.
Y by Adventure10, Mango247
in a quadrilateral 
, 
and 
are on 
and 
respectively such that the area of triangles 
and 
is 
of the area of . 
is the intersection point of digonals of . 
and 
.
a) in what ratio does
cut the digonals?(13 points)
b) find
.(5 points)
, 
and 
are on 
and 
respectively such that the area of triangles 
and 
is 
of the area of . 
is the intersection point of digonals of . 
and 
.a) in what ratio does
cut the digonals?(13 points)b) find
.(5 points)
![$[ABC]=\frac{5}{11}[ABCD]$](http://latex.artofproblemsolving.com/7/f/d/7fd478bff5e4e321c1dd942a2fa39643bd2b1361.png)
and ![$[BDC]=\frac{5}{8}[ABCD].$](http://latex.artofproblemsolving.com/2/e/2/2e2e482507d5c1aa215813eaa670b1d2d71b4468.png)
for part 
![$\in [BC]$](http://latex.artofproblemsolving.com/4/e/d/4ed241bef261bc9497520d240afa4857d62481bf.png)
so I agree with oneplusone.
we have also a negative ratio.
