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 Smile! "It is impossible for a man to learn what he thinks he already knows" -- Epictete Math Shortcuts The radii of circumscribed (R) and inscribed (r) circles within regular polygons of n sides, each of length x, are given by: (x/2) csc(180°/n) and (x/2) cot(180°/n)
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# Previous Puzzles of the Month + Solutions

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Puzzle # 125

A mathematical shield

Once upon a time, Mars, the God of war, intended to test the IQ of the goddess Minerva. So, showing his shield, he told her: "Darling, on my shield, there are 3 equal circles which represent the qualities of the warrior: strength, flexibility, and decisiveness. As you can see, one of the circles has been scratched by a sword, and the resulting score is three inches long (line AB in the illustration). Can you then tell me what is the area of my shield?".
Find the very shortest way to solve this puzzle and use only basic geometry, trigonometry is not allowed!

Difficulty level: , basic geometry knowledge.
Category: Geometrical puzzle.
Keywords: inscribed circles, incircles.
Related puzzles:
- Achtung Minen!

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