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Sangaku of Hie-shrine/日枝神社 算額 Mystery Cache

Hidden : 11/2/2016
Difficulty:
3.5 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:

Saitama Festival 2016 Memorial Cache-The 彩ンはVVVV  シブイ ぞ サイタマ!


Sangaku is a big Ema (votive picture tblet) dedicated to a shrine almost in the Edo era and Meiji era and many  questions in mathematics (Japanese mathematics) are written in it. Existing Sangaku is approximately 900 faces and 87 faces are left in Saitama pref.. It is the third heighest in Japan. By the way, Fukushima pref. is 111 faces which is the first,  Iwate pref. is 97 faces which is the second, Gunma pref. is 77 faces which is the fourth, but Tokyo jumps to 385 faces and get the commanding lead when the loosed Sangaku add. However, unfortunately most of them are destroyed by the war fire, and only 16 faces are left now. The cache is hidden in Hie shrine where a Sangaku is dedicated in Saitama pref.. 
Solve the question (cf. attached figure) writen in the Sangaku and please find out the cache.

算額は、主に江戸から明治に掛けて神社に奉納された大型の絵馬で、それには様々な数学(和算)の問題が書かれています。
現存する算額は凡そ900面ですが、埼玉県には87面が残っており、全国3位となっています。 因みに、1位は福島県111面、2位岩手県97面、4位群馬県77面となりますが、遺失した算額を加えると東京都が385面と断トツに躍り出ます。 しかしながら、残念なことに大半が戦火により焼失し、現在は16面しか残っていません。
キャッシュは算額が奉納されている埼玉県の日枝神社に隠しました。 その算額の問題(添付図参照)を解いて、キャッシュを探し当ててください。

As shown in the attached figure(Gallery), two isosceles triangles, two circles 甲 and six circles 乙 are the inside of a circle. The diameter of the circle 乙 is 1 inch, then how many inches is the diameter (D甲) of the circle 甲 and the diameter (Do) of the outer circle?   

下図のように、円の中に二等辺三角形二つ、甲円二つと乙円六つがあります。乙円の直径が1寸の時、甲円の直径 (D甲)と外円の直径(Do)は何寸ですか?

The cache is in the place which is (D甲x3.7)m to the southeward and (Ddx0.94)m to the eastward from the GZ. 

 

text

Additional Hints (Decrypt)

sbzhyn (fcbvyre)

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)