are there such that 
and 
?
, where 
is a real number. Prove that for all positive 
then prove
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 
.
that satisfy 
with orthocenter 
.
to meet 
.
meets the midpoint of 
.
,
.
Y by Mango247, Mango247, Mango247
The radius 
of the circle with center 
intersects the perpendicular bisector of the chord 
at the point 
. Through some point of the circle 
, there are lines 
, intersecting at a single point 
, and 
, intersecting the circle at a single point 
Prove that 
.
of the circle with center 
intersects the perpendicular bisector of the chord 
at the point 
. Through some point of the circle 
, there are lines 
, intersecting at a single point 
, and 
, intersecting the circle at a single point 
Prove that 
.
