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such that p is a prime, 
and 
is a divisor of 
.
such that![\[ \frac {2^n + 1}{n^2}
\]](http://latex.artofproblemsolving.com/9/2/2/922444e7669c326efcad5fde3ea00f8c2d9fa5d8.png)
is an integer.
on a circle and points 
and 
on segment , such that 
Find the ratio 
, where 
is a point on arc , such that 
is maximized.
let 
and 
be the altitudes. Let the points 
and 
fulfil the following requirements:
is the circumcentre of triangle .
and 
are equal to the circumradius of triangle .
has the same direction as the oriented segment 
. Similarly, 
has the same direction as 
, and 
has the same direction as . is the incentre of triangle .
be an isosceles triangle such that 
and 
. Let be the foot of the altitude from and let 
be a point on the side 
such that 
. Determine the measure of the angle 
.
be an isosceles triangle such that and . Let be the foot of the altitude from and let be a point on the side such that . Determine the measure of the angle .
