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 
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 
.
,
.
.
is selected on the diagonal 
such that 
.
as 
.
.
as 
respectively, compute the area of 
given the area of 
.
.
is equilateral. Given that 
and the midpoint of 
Y by Adventure10, Mango247
Let 
be a parallelogram in the plane. We draw two circles of radius 
, one through the points 
and
, the other through and 
. Let 
be the other intersection point of the circles. We assume that is not a vertex of the parallelogram. Show that the circle passing through 
, and also has radius .
be a parallelogram in the plane. We draw two circles of radius 
, one through the points 
and
, the other through and 
. Let 
be the other intersection point of the circles. We assume that is not a vertex of the parallelogram. Show that the circle passing through 
, and also has radius .This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 1:31 AM
)
.
(here we have used the usual vector notation). Alternatively, we may translate 
to 
)
is cyclic (using the fact that, by the constructionn, quadrilaterals 
and 
are parallelograms along with 
