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
A person of height 
metres leaves a tall building at ground level and walks in a straight line direction up a path of constant gradient. He walks under a tall billboard after twenty metres and continues walking up the path for another five metres at which point he turns around and notices that the top of the billboard aligns horizontally with the top of the building. Then continues along up the path a further ten metres where he turns around again and notices that the top half of the building is now visible above the billboard. The height of the building is much greater than the height of the billboard which is much greater than the height of the person. What is the height of the building?
metres leaves a tall building at ground level and walks in a straight line direction up a path of constant gradient. He walks under a tall billboard after twenty metres and continues walking up the path for another five metres at which point he turns around and notices that the top of the billboard aligns horizontally with the top of the building. Then continues along up the path a further ten metres where he turns around again and notices that the top half of the building is now visible above the billboard. The height of the building is much greater than the height of the billboard which is much greater than the height of the person. What is the height of the building?This post has been edited 2 times. Last edited by parmenides51, Jan 2, 2021, 5:39 AM
Reason: typo, straight word
Reason: typo, straight word
.
as his head's initial position.
as his head's position after climbing 20 m
as his head's position after climbing an additional 5 m
as his head's position after climbing an additional 10 m
are collinear
as the top of the building, which is vertically above 
.
and 
are similar, but they have ratio 
.
is vertical, the point 
.
gives 
