,
and 
,
is the least common multiple of the numbers 
.
for every positive integer 
.
,
,
,
,
,
positions to the right. Andrés and Beto alternate turns, starting with Andrés. The winner is the player who moves a token into the rightmost cell. Determine who has a winning strategy in terms of 
.
,
on side 
passing through 
at point 
Y by
You are given an acute-angled triangle 
. Let us denote by 
the perpendicular bisector of 
. A straight line parallel to 
and passing through point 
intersects at point 
, and a line parallel to 
and passing through point 
intersects at point 
. It turned out that 
divides 
in half. Prove that the altitude of triangle from vertex 
, divides 
in half.
. Let us denote by 
the perpendicular bisector of 
. A straight line parallel to 
and passing through point 
intersects at point 
, and a line parallel to 
and passing through point 
intersects at point 
. It turned out that 
divides 
in half. Prove that the altitude of triangle from vertex 
, divides 
in half.This post has been edited 1 time. Last edited by parmenides51, Nov 1, 2020, 8:38 AM
