be a set of Natural numbers from 
to 
.
)
.
and 
,
is not less than the area of 
,
inequalities, these given comparisons satisfy the following three constraints:
and 
,
and 
respectively, then the sum of elements of the union 
is greater than that of 
.
that satisfies all these conditions?
.
then prove \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2}\cdot\frac{abc}{ab+bc+ca}\ge \frac{5}{3}.$$
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 
.
that satisfy 
with orthocenter 
to meet 
.
meets the midpoint of 
.
,
.
Y by
On the side 
of the square 
, the point 
is chosen and the equal squares 
and 
are constructed (
and 
lie inside the square). Let 
be the midpoint of 
, 
is the incenter of the triangle 
. Prove that:
a) the points
lie on the same circle;
b) the circles inscribed in triangles and 
have the same radii.
of the square 
, the point 
is chosen and the equal squares 
and 
are constructed (
and 
lie inside the square). Let 
be the midpoint of 
, 
is the incenter of the triangle 
. Prove that:a) the points
lie on the same circle;b) the circles inscribed in triangles
and 
have the same radii.This post has been edited 3 times. Last edited by parmenides51, Apr 26, 2022, 9:48 PM
