There are a number of different geometric centers that are
common to all triangles, two of which are the orthocenter and the
incenter.
The Orthocenter is
defined as the point at which the three altitudes of a triangle
intersect. An altitude of a triangle is represented by a straight
line drawn through the vertex and perpendicular to the opposite
side
.
The incenter of a triangle is the point at which the bisectors
of each of the three angles intersect. An angle bisector is a line
drawn through a vertex which cuts the corresponding angle in
half.
To find the cache you must first find the orthocenter of the
triangle formed by points A,B and C whose coordinates are listed
below. Once you have found the orthocenter that will become Point
O. The cache can then be found at the incenter of the triangle
formed by points A,B and O.
Due to the complexities of two different triangles and fairly
long distances, there could be plotting errors of as much as 200 to
300 ft at the cache therefore FizzyCalc
was used for high accuracy. Using FizzyCalc and good plotting
techniques will get you good results.
No complicated trigonometric functions such as sine, cosine etc.
were used to set this up and none should be needed to solve it.
General math should suffice.
- Point A N 42 18.830 W 71 29.934
- Point B N 42 18.830 W 71 26.655
- Point C N 42 19.537 W 71 27.807
Please make sure the cache is hidden when you leave. Thanks.
Congrats to CheckerMan for first to
find.