are there such that 
and 
?
, where 
is a real number. Prove that for all positive 
then prove
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
is the incentre and point 
is defined such that 
and 
is the perpendicular bisector of 
and 
be the circles passing through 
and 
respectively such that 
is tangent to 
to be a point such that it lies on both the circles 
and 
are perpendicular.
weights, each weighing 
and another 
weights with 
each. Write a algorithm that determines the ways in which a scale can be balanced with a weight 
on the left pan, and display the number of possible solutions. (The weights can be placed on both pans and the program starts with the numbers 
.
that satisfy 
with orthocenter 
.
to meet 
.
meets the midpoint of 
.
,
.
Y by
A game is played by two players on an infinite plane containing 
pieces, 
sheep and 
wolf. The first player starts the game by moving the wolf. Then the second player moves some sheep, and so on. On each move, a piece can move up to a distance of meter. Is it true that, regardless of the initial position of the pieces, the wolf always manages to capture at least one sheep?
pieces, 
sheep and 
wolf. The first player starts the game by moving the wolf. Then the second player moves some sheep, and so on. On each move, a piece can move up to a distance of meter. Is it true that, regardless of the initial position of the pieces, the wolf always manages to capture at least one sheep?This post has been edited 2 times. Last edited by parmenides51, Aug 2, 2021, 11:55 AM
