# Searching Geometry Mystery Cache

Hidden : 10/09/2010
Difficulty:
Terrain:

Size:  (small)

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## Geocache Description:

Lundy Jack the pirate has treasure hidden in the hills of South Birmingham. What place would be safer from the grubby fingers of other pirates than the middle of this island?
Unfortunately Lundy Jack hired a mathematician to create the treasure map for him and now he can't work out where the treasure is! Some distances are marked on the map but not those that lead to the treasure.
Poor Lundy Jack can't make head nor tail of it. Can you help?

Note:
This puzzle uses British National Grid, not Latitude and Longitude.
If your GPSR has an option to switch to the British coordinate system (sometimes labelled as BNG or EPSG 27700) you can choose this option in your GPSR settings. If you don't have this option, don't worry. You just need to convert your grid reference to lat-long before you set out. See the note at the bottom of this listing.

The map looks simple enough: the home location (point H) has a grid reference. All you need to do is *add* the horizontal distance (line HB) to the easting and *subtract* the vertical distance (line BC) from the northing to locate point C.

However, Lundy Jack knows the map is deliberately not to scale. So you can't use a rule to measure distances or a protractor to measure angles and scale these up or down to determine the length of other lines or the size of other angles.
To find the horizontal and vertical distances you need to use some of the laws of geometry. These laws are taught in GCSE mathematics. For those in need of a refresher, have a look at this useful index of theorems (specifically theorems 4, 5, 8, 10, 12).

Whilst walking the plank the mathematician did reveal that:
"The lengths HG, GB and CA are in metres" and "all the lines are straight except for the obvious curve, which is a circle with point E at its centre ... remember, it's not to scale, so the circle may not look precisely circular."
So we know that line DEF is straight, line DGBAJK is straight, and so on.
At this point, however, Lundy Jack (who has always despised modern fangled things such as metric and decimalisation) lost his patience and threw the mathematician to the sharks. A loss of temper that Lundy Jack now regrets but maybe he can rely on you to locate his booty.

Before you set out ...

You should have a two-letter and ten-digit grid reference for the cache: SP _____ _____. Try using this grid reference conversion tool to convert this to a lat-long and check your lat-long answer here.

There are no swaps in the cache, just pieces of eight.
If you are successful in finding the treasure, take a piece of eight for your troubles (no need to leave a swap behind) ... and don't forget to let Lundy Jack know his treasure is still safely hidden by logging your find here!