[/quote]
,
let 
and 
be the circles passing through 
and 
respectively such that 
to be a point such that it lies on both the circles 
and 
are perpendicular.
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
with circumcircle 
is given. Let 
be the midpoint of 
be the foot of altitude from 
be the intersection point of 
.
lies on the arc 
.
.
with diameter 
meets 
(where 
)
is perpendicular to 
.
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 
.
![\[ x + y^2 = p^m \]](http://latex.artofproblemsolving.com/e/c/f/ecf553036f22327dd457dc06611b6bc1b0ef072c.png)
![\[ x^2 + y = p^n \]](http://latex.artofproblemsolving.com/5/b/d/5bd672934a395aabd6865ca4b50d8da75c0fe07e.png)
For 
positive integers and 
being a prime.
and 
.
Equality holds when 
or 
.
intersect again at 
.
to meet 
meets the midpoint of 
,
.
Equality holds when 
.
determine a triangle 
,
is relative to 
are concurrent at a point 
and that 
lie in the interiors of segments 
respectively, such that 
Let 
intersect 
at 
intersect 
at 
.
and 
are either parallel or coincide.
and 
.
Where 
Y by Adventure10, Mango247
Let 
be a quadrilateral with 
parallel to 
, the angles 
and 
right and such that the angle 
is right , where 
is the midpoint of 
. Let 
be the foot of the perpendicular to 
that passes by 
the intersection point of 
with 
and 
the intersection point of 
with 
. Show that the angle 
is right , and that 
be a quadrilateral with 
parallel to 
, the angles 
and 
right and such that the angle 
is right , where 
is the midpoint of 
. Let 
be the foot of the perpendicular to 
that passes by 
the intersection point of 
with 
and 
the intersection point of 
with 
. Show that the angle 
is right , and that 
This post has been edited 3 times. Last edited by parmenides51, Jun 21, 2022, 1:42 AM
