blocks, each weighing at least 
;
.
with 
you can choose a subset of the blocks whose total weight is at least 
.
such that 
.
chessboard. Initially, Azer colors all cells of this chessboard with some colors. Then, Babek takes 
rows and 
cells in the intersection. Babek wants to have all these 
be non-negative real numbers such that 
Prove that
be a circle, and let a line 
intersect 
and 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
and 
Prove that
.
Prove that
and 
Prove that
,
,
is not greater than 
.
.
.
and 
be points on a plane such that 
,
be the set of all points 
,
is a real number. The path that 
Y by
There are three cones on the table, touching each other. The radii of their bases are equal to 
and 
. A truncated cone, which has a common generatrix with each of the other cones, was placed on the table with the smaller base down. Find the radius of the smaller base of the truncated cone.
and 
. A truncated cone, which has a common generatrix with each of the other cones, was placed on the table with the smaller base down. Find the radius of the smaller base of the truncated cone.This post has been edited 1 time. Last edited by parmenides51, Feb 14, 2021, 5:46 PM
