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 
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 
.
that satisfy 
with orthocenter 
.
to meet 
.
meets the midpoint of 
.
,
.
Y by Mango247
Let 
and 
be two circles such that 
passes through 
. Point 
lies on such that 
. The tangents from at meet again at 
and 
. Prove that the tangents from and at 
- others than 
and 
- meet at a point located on .
and 
be two circles such that 
passes through 
. Point 
lies on such that 
. The tangents from at meet again at 
and 
. Prove that the tangents from and at 
- others than 
and 
- meet at a point located on .This post has been edited 2 times. Last edited by parmenides51, May 16, 2020, 11:39 PM
.
are tangents to 
are tangents to 
(that doesn't contain 
(that doesn't contain 
