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## The Peak at the Orthocenter

A cache by Wily Javelina
Hidden : 2/18/2003
In Arizona, United States
Difficulty:
Terrain:

Size:  (regular)

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### Geocache Description:

This geocache is located on top of a small peak near the Tucson Mountains. From the information provided below you will have to calculate the true location of the cache.

In a triangle, an altitude is the line that runs between the vertex and the perpendicular line opposite of the vertex. The altitudes for the triangle below are in red. The three altitudes intersect at a point - the point is called the orthocenter. The orthocenter for the triangle below is the point labeled O.

The geocache is located at the orthocenter of the triangle defined by the three vertices ABC below:

1. N 32° 16.407' W 111° 08.839'
2. N 32° 11.057' W 111° 03.658'
3. N 32° 18.238' W 111° 00.373'

The math calculations are not very difficult, that is, once you get the problem set up. Note that the coordinates provided at the top of the page are not the location of the cache, though, they do provide a convenient parking location for the approach to the cache. There is a faint trail leading to the base of the peak from the parking location, it is roughly a 0.7 miles hike to the cache from there. I approached the summit from the West saddle, it looked like the most appealing route up...and it was. This small peak was a lot of fun to climb and was very aesthetically pleasing, too bad it is not ten times higher. The cache container is made of 3" PVC pipe, painted tan, and is very well hidden.

A note about the ratings: I am not so sure that this is really a five-star Difficulty cache, probably a hard four. I will let you, the geocaching community, decide. I don't want to sandbag anybody, so I will leave the rating conservative for now.

(5/18/03) I haven't recieved any feedback on the Difficulty rating, so I think will leave it as is. A while back I did up the Terrain rating from 4 stars to 4.5 stars.

### Inventory

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