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 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 
.
with orthocenter 
.
to meet 
.
meets the midpoint of 
.
,
.
with side length of 
.
is selected on the diagonal 
such that 
.
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 Adventure10, Mango247
The diagonals of the inscribed convex quadrilateral 
intersect at the point 
. Let 
be a line dividing the angle 
in half. Denote by 
the nondegenerate triangle formed by the lines 
. Let 
and 
. Prove that the circumscribed circles of the triangles 
and 
are tangent to each other.
intersect at the point 
. Let 
be a line dividing the angle 
in half. Denote by 
the nondegenerate triangle formed by the lines 
. Let 
and 
. Prove that the circumscribed circles of the triangles 
and 
are tangent to each other.
