,
an integer, that lie within the polygon is equal to the sum of the lengths of the segments of lines of the form 
,
,
,
intersects a circle at exactly two points 
and 
.
is extended beyond 
such that 
.
intersect at the point 
.
is cyclic. (4)
ascertain whether among its first 
terms there is a number that ends with four zeros.
straight lines in general position are drawn on the plane. Prove that among the parts into which they divide the plane, there are at least 
triangles
and 
such that 
pupils is organised into 
clubs , so that each club contains 
pupils and no two clubs have the same composition. Prove that there are two clubs which have exactly one common member.
of its volume is below the water level, while more than half of its surface area is above the water level?
red points divide a blue circle into 
to 
Y by
On the plane we mark 
(
) straight lines passing through one point 
in such a way that for any two of them there is a marked straight line that bisects one of the pairs of vertical angles, formed by these straight lines. Prove that the drawn straight lines divide full angle into equal parts.
(
) straight lines passing through one point 
in such a way that for any two of them there is a marked straight line that bisects one of the pairs of vertical angles, formed by these straight lines. Prove that the drawn straight lines divide full angle into equal parts.This post has been edited 1 time. Last edited by parmenides51, Sep 17, 2024, 2:13 PM
