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Mystery Cache

Equilateral Triangle - South

A cache by SlideRule Send Message to Owner Message this owner
Hidden : 9/2/2006
In Chile
4.5 out of 5
1 out of 5

Size: Size: micro (micro)

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Geocache Description:




With a name like SlideRule, you know sooner or later there would be a problem of mathematical nature.

So here is today's problem:

In plane geometry, from any given two points, you can construct a line segment.  From that line segment, it is easy to construct an Equilateral Triangle.


Now, start with two points on the globe. 

Point 1 S 13.556243643131 W 116.730255858190
Point 2 N 07.464291909245 W 075.221183660873

Using  those two points as one of the sides, construct an Equilateral Triangle using points on the surface of the Earth.  At the vertex of the triangle produced, there is the cache location.


Assumptions: (For the calculations)

  • Perfectly Spherical Earth (NOT Ellipsoidal)

  • This is a pure Euclidian geometry problem.

  • The accuracy that I give you is excessive.  Close to a millimeter.  

  • Notice that the coords are in Decimal Degrees, Not in DD MM.MMM fromat.

  • The resultant triangle is the results of equal secants drawn from point to point.

Some of you may suggest: 

  1. The Earth is not a perfect Sphere: That is true.  For this problem, assume that the Earth is a perfect sphere, Therefore, You can safely make the assumption that the Lat/Lon that you get as the solution to this problem  There will be a non-spherical problem in the future.  I will post the link [Here] after I position the caches.

  2. That given the two points, there are two solutions:  Well, guess what boys and girls?  There are two caches.  One generally North of the line between the two points and another South of the line drawn between the two points.

For You Information:  There are two Caches...

 Equilateral Triangle - South [GCY3H2]

 Equilateral Triangle - North [GCNAJX]  

Solve, or better yet, Find them both for the big EGO trip.


Now for a few hints:

  • The Checksum for the North Cache is: N 16 and W 26 in DD MM.MMM format

  • The Checksum for the South Cache is: S  28 and W 41 in DD MM.MMM format

  • The LSD for the North Cache is 0 and 6,  For the South Cache is 8 and 7.


  • The caches are both large Ammo sized boxes painted International orange with UV and Light reflectors, cleverly camoed to look like a small black magnetic Hide-A-Key.  Bring your own writing utensil.

  • Owner requests that finders not inform others of the location of this Cache.  This is to maintain the difficulty of the Cache.

  • All feedback about the coords and the cache hide will be appreciated.

Additional Hints (Decrypt)

Email owner the coords before going out to find this cache

Decryption Key


(letter above equals below, and vice versa)



12 Logged Visits

Found it 6     Write note 2     Post Reviewer Note 1     Publish Listing 1     Owner Maintenance 2     

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**Warning! Spoilers may be included in the descriptions or links.

Current Time:
Last Updated: on 1/25/2017 8:58:36 AM (UTC-08:00) Pacific Time (US & Canada) (4:58 PM GMT)
Rendered From:Unknown
Coordinates are in the WGS84 datum

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