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Coins on a Jar

Consider a round jar with no lid. The radius of the opening in the
jar is 10. A coin (with a radius R < 10) can be placed flat on the edge of
the jar without falling.
The coin can be placed such that its center is on the rim of the jar, or
it can be moved toward the center of the jar.
- What is R, when the coin is as close to the center of
the jar as possible without falling in, and the inside edge of the coin
is at the center of the jar's opening?

A number of identical coins are placed around the rim of the jar, each
touching a coin on either side.
- What are the possible values of R if the center of each coin is on
the rim of the jar?
- What are the possible values of R if each coin is as close to the
center of the jar as possible?
- Are there any size coins which can be placed in
**both** of the
previous two arrangements (with a different number of coins in each)?

Source: Original.

Solution

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