[/quote]
,
that satisfy the equation 
.
be a circle, and let a line 
intersect 
and 
Circles 
and 
are internally tangent to 
and 
respectively, and both are tangent to 
Similarly, circles 
and 
are externally tangent to 
and 
respectively.
the segment 
has a length of 
and 
find the length of segment 
be a scalene triangle with circumcircle 
and circumcircle 
.
and 
as the midpoints of 
and 
,
to 
.
meets 
,
intersects 
.
at 
and 
at 
.
intersect 
,
intersect 
.
is the reflection of 
and 
lies on the circumcircle of 
.
be real numbers such that 
and 
and determine the equality cases.
be positive real integer such that 
Prove that
such that 
and 
satisfying :![\[n^{2p}=m^2+n^2+p+1\]](http://latex.artofproblemsolving.com/7/4/e/74ee592cb8b3f3a3996ea34f40b78fde9d3672fc.png)
and 
are integers and 
is a prime number.
and 
Prove that
Approach: I'm trying to factor 
to get 
.
such that 
divides 
.
![$a,b,c \in [-\frac{1}{2}, \frac{1}{2}]$](http://latex.artofproblemsolving.com/5/0/b/50bc691baa4e4bbef868e4799929c8c93d1b6f1a.png)
.
Let ![$a,b,c \in [-2,2]$](http://latex.artofproblemsolving.com/8/0/6/8066d4353091772c401e3e34f5499a8fa2bd9991.png)
.
be positive real numbers such that 
Prove that 
.
Y by centslordm
A light hitting a mirror at angle 
measured from the perpendicular is reflected at angle on the other side of the perpendicular. The rough diagram here shows a cross section of the pentagonal prism found in some cameras, where sides 
and 
are mirrors and the angles 
and 
are equal. Light entering the prism is reflected twice, and emerges at 
to its original path. What is the angle
?
measured from the perpendicular is reflected at angle on the other side of the perpendicular. The rough diagram here shows a cross section of the pentagonal prism found in some cameras, where sides 
and 
are mirrors and the angles 
and 
are equal. Light entering the prism is reflected twice, and emerges at 
to its original path. What is the angle
?This post has been edited 3 times. Last edited by parmenides51, Feb 26, 2021, 11:30 PM
