This is the first in a series of caches based on the "Concurrence Theorems". In this case, the theorem states that "The perpendicular bisectors of the sides of a triangle are concurrent" (that is, they all pass thru the same point). The point of concurrence is the circumcenter of the triangle.
My two "Midpoint" caches each required you to find a point equidistant from two specified points. That point is known as the midpoint of the segment joining the two points. When a third point is introduced, the situation becomes considerably more complicated.
(The following discussion assumes we are talking about points in a plane--i.e., plane geometry.)
For any three non-collinear points (that is, points that are not in a line), there is exactly one point equidistant from each of them. That point is known as the circumcenter, so named because it is the center of a circle passing thru each of the three points (the "circumcircle"). The three points determine a triangle, and the circle is said to be "circumscribed" about the triangle. In geometric constructions, the simplest way to find the circumcenter of a triangle is to construct the perpendicular bisectors of any two sides of the triangle; the circumcenter is the point where those perpendicular bisectors intersect. (I love Geometry!)
This cache is located at the circumcenter of triangle ABC. Point A is the posted coordinates; point B is N35°33.274',W82°43.237'; and point C is N35°31.676',W82°43.900'. Let me just say that the math involved in calculating the circumcenter coordinates is not simple.
There is nothing special at the actual cache location. No wonderful view. Just a mundane park-n-grab location. Well, there is a small FTF prize. But good luck finding it. You're looking for an Altoids tin. tiny plastic container (Icebreakers).
You can check your answers for this puzzle on Geochecker.com.
Note: when checking on this on 6/23/14, I was approached by the manager who pointed out that they have video surveillance of the whole place so they could see me. She of course had no idea what I was doing, but I explained it to her and showed her the cache. So searchers should be aware that they are in view of surveillance cameras, and inside personnel *might* be aware of what is going on...