[/quote]
,
and 
.
and 
.
Equality holds when 
or 
be a cyclic quadrilateral whose opposite sides are not parallel. Suppose points 
lie in the interiors of segments 
respectively, such that 
Let 
intersect 
at 
,
intersect 
at 
.
and 
are either parallel or coincide.
.
Where 
such that :
.
be reals such that 
Prove that 
Let 
Prove that 
be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
colors, such that among any 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
This easy via the binomial theorem for the quantity is just 
,
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 
.
and let 
and 
in line 
respectively. A line through 
and 
respectively such that 
and 
are tangent to each other.
Y by Adventure10, Mango247
Given a triangle 
, let 
be the point where the incircle of the triangle touches the side 
. A circle through the vertices 
and 
is tangent to the incircle of triangle at the point 
. Show that the line 
passes through the excentre of triangle corresponding to vertex 
.
, let 
be the point where the incircle of the triangle touches the side 
. A circle through the vertices 
and 
is tangent to the incircle of triangle at the point 
. Show that the line 
passes through the excentre of triangle corresponding to vertex 
.
,
is the polar of 
.
,
,
are collinear.
is harmonic , 
,
,
.
