and 
.
be the set of all positive integers. Determine all subsets 
of 
such that
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
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 
.
.
to meet 
.
meets the midpoint of 
.
,
.
with side length of 
.
is selected on the diagonal 
.
as 
.
.
as 
respectively, compute the area of 
given the area of 
.
.
lies inside the rectangle such that 
is equilateral. Given that 
and the midpoint of 
Y by
Given an acute triangle 
. A circle inscribed in a triangle with center at point 
touches the sides 
at points 
and 
, respectively. The lines 
and 
intersect at the point 
. Prove that the circles circumscribed around the triangles 
and 
are tangent.
(Dmitry Shvetsov)
. A circle inscribed in a triangle with center at point 
touches the sides 
at points 
and 
, respectively. The lines 
and 
intersect at the point 
. Prove that the circles circumscribed around the triangles 
and 
are tangent.(Dmitry Shvetsov)
This post has been edited 1 time. Last edited by parmenides51, Oct 9, 2020, 12:37 PM
