Find the smallest possible positive value of such that
If can be represented by where is square free and are integers. Find .
How many real numbers satisfy
A square of side length contains unit circles at each of corners and such that each circle is tangent to the square at precisely two points. A ray of light emanating from point reflects off each circle and then returns to , creating a path in the shape of an equilateral triangle.
There is a unique value of for which this scenario can occur. Find .
Note: "Reflecting" means that the angle of incidence equals the angle of reflection.
It is the case that for some integer . Find .
Find the sum of all such that