attaining all positive values and positive numbers 
are given. Numbers 
satisfy
for every 
.
satisfying 
.
that satisfy 
with 
,
and area 
.
with diameter 
meets 
at 
.
,
and extend to meet 
such that 
and 
is the diameter of 
of 
,
of 
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
.
lie on 
respectively, such that 
.
to meet the circumcircle of 
respectively. Let the circumcircles of 
meet at points 
.
to 
,
,![$[ABC]$](http://latex.artofproblemsolving.com/d/3/3/d33cc80fa8f093e155c5be46d2e5d9da3d7e1ef5.png)
.
with 
,
.
to meet the circumcircle of 
at 
,
.
Y by Adventure10, Mango247
There are 
lines on the plane in general position; Meaning any two of them meet, but no three are concurrent. All their intersection points are marked, and then all the lines are removed, but the marked points are remained. It is not known which marked point belongs to which two lines. Is it possible to know which line belongs where, and restore them all?
Proposed by Boris Frenkin - Russia
lines on the plane in general position; Meaning any two of them meet, but no three are concurrent. All their intersection points are marked, and then all the lines are removed, but the marked points are remained. It is not known which marked point belongs to which two lines. Is it possible to know which line belongs where, and restore them all?Proposed by Boris Frenkin - Russia
in the set of marked points 
(
points, such that these two sets of points form two separate straight lines with 
points in the plane, and each line consists of 
points, as no three lines are concurrent (i.e. This plane has maximum possible no. of points in a plane of 
,
points.
.
lines with the maximum no. of intersections, and further there are 
,
collinear intersection points. Indeed, given any 
.
