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 
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 
.
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 a semicircle is given with diameter 
and centre 
and let 
be a arbitrary point on the segment 
. Point 
on the semicircle is such that 
is perpendicular to . A circle with centre 
is tangent to the arc 
at 
and to the segment and at 
and 
respectively. Prove that the triangle 
is isosceles.
and centre 
and let 
be a arbitrary point on the segment 
. Point 
on the semicircle is such that 
is perpendicular to . A circle with centre 
is tangent to the arc 
at 
and to the segment and at 
and 
respectively. Prove that the triangle 
is isosceles.
and power 
;
,
,
,
to 
,
collinear. Note 
,
is tangent to 
and we are done.
.
and 
with 
radius, 
and 
,
,
and we are done.
