[/quote]
,
= 2∠AMP.
,
not dividing any of them, and an integer 
such that if one considers the infinite sequence 
and looks at the highest power of 
)
.
be a positive integer. Consider 
points on the circumference of a circle.
}
and 
in this set at last in one of the permutation
:
convex polygons, determine the maximum possible number of edges in the obtained figure.
vertices and 
edges in the resulting figure, then 
.
.
.
be an inscribed quadrilateral. Circles of diameters 
and 
intersect at points 
and 
,
and 
intersect at points 
and 
.
and 
intersect in two points 
and 
.
and 
are concurrent.
be distinct real numbers such that 
Find the value of 
Find the value of 
Find the value of 
for which there exists a sequence 
of positive integers satisfying the following conditions:[list]
for all integers 
for all integers 
the sequence 
is a permutation of
[/list]
.
be a cyclic quadrilateral. Let 
be the midpoint of the arc 
of its circumcircle which does not contain 
or 
.
and 
meet at 
and the lines 
and 
meet at 
.
and 
Y by Adventure10
Let 
be a pentagon inscribe in a circle 
. Let 
. Suppose the parallel line with 
which passes through 
which cut 
at 
. If 
be the circumcircle of triangle 
then prove that is tangent to .
be a pentagon inscribe in a circle 
. Let 
. Suppose the parallel line with 
which passes through 
which cut 
at 
. If 
be the circumcircle of triangle 
then prove that is tangent to .This post has been edited 2 times. Last edited by War-Hammer, Sep 6, 2013, 10:04 PM
by a combination of cyclic quads and parallel lines, so quadrilateral 
must be cyclic. Therefore 
and 
.
and 
are homothetic with center of homothety 
,
and 
are outside 
are concyclic, hence 
,
being the common angle value. Seeing that 
we infer that the circumcenter of 
belongs to 
,
meet the circumcircle of 
is cyclic but 
,
,
to 
at 
,
to circle 
concyclic.So 
or 
.
is Tangent to 
