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 
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 
.
is selected on the diagonal 
such that 
.
as 
.
Y by
You have a semicircle with diameter 
of length 
cm, inside which are drawn non-overlapping semicircles of diameters 
cm and 
cm. A circle 
is drawn, touching all three semicircles as shown. Show that the perpendicular distance from the centre of this circle to the diameter is equal to the diameter of the circle .
of length 
cm, inside which are drawn non-overlapping semicircles of diameters 
cm and 
cm. A circle 
is drawn, touching all three semicircles as shown. Show that the perpendicular distance from the centre of this circle to the diameter is equal to the diameter of the circle .This post has been edited 1 time. Last edited by parmenides51, Jan 20, 2021, 2:38 PM
with radius 
such that circle 
with descartes' theorem
