and 
.
Equality holds when 
or 
and 
,
cookies from one of the piles, of which he eats 
and puts 
for which Marica has a winning strategy.
be non-negative real numbers such that 
Prove that
is defined such that 
and 
is the perpendicular bisector of 
and 
be the circles passing through 
and 
respectively such that 
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 
.
.
to meet 
meets the midpoint of 
.
,
.
with side length of 
.
such that 
.
as 
.
.
as 
respectively, compute the area of 
given the area of 
.
.
is equilateral. Given that 
and the midpoint of 
a
.
Y by Adventure10
Let 
be the incenter and 
the shortest side of the triangle 
. The circle centered at passing through 
intersects the ray in 
and the ray 
in 
. Let 
be the point of tangency of the 
-excircle of the triangle with the side 
. Let 
be the reflection of with respect to the point . Prove that 
.
be the incenter and 
the shortest side of the triangle 
. The circle centered at passing through 
intersects the ray in 
and the ray 
in 
. Let 
be the point of tangency of the 
-excircle of the triangle with the side 
. Let 
be the reflection of with respect to the point . Prove that 
.This post has been edited 1 time. Last edited by Steff9, Jun 11, 2017, 10:42 AM
Reason: latex
Reason: latex
and 
.
,
