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 
.
.
to meet 
.
meets the midpoint of 
.
,
.
with side length of 
.
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
Let 
be the angle bisector of the acute-angled triangle 
. and 
be the circle circumscribed about it. Denote by 
the intersection point of the extension of the altitude 
of the triangle with the circle . Prove that if 
, then 
.
be the angle bisector of the acute-angled triangle 
. and 
be the circle circumscribed about it. Denote by 
the intersection point of the extension of the altitude 
of the triangle with the circle . Prove that if 
, then 
.This post has been edited 2 times. Last edited by parmenides51, Sep 6, 2018, 8:49 AM
Reason: latex
Reason: latex
,
,
.
.
(they are on the same arc), so 
.
