perplexus.info :: Geometry : On The Edge

On The Edge (Posted on 2004-10-24)

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?

Submitted by Brian Smith

Rating: 3.0000 (6 votes)

Solution: (Hide)

When the coin is as close to the center as possible, the endpoints of a diameter of the coin must be touching the jar rim.
There is a right triangle then from the center of the jar to the center of the coin to one of the end points where the jar rim and coin touch with sides Rcoin, Rcoin, and Rjar.
Thus the radius of a coin in this configuration is Rjar/sqrt(2). If Rjar is 10, Rcoin is 5*sqrt(2).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Owl seems to have it	Steve Herman	2004-10-26 11:27:51
re: Maybe Solution	SteveH	2004-10-24 17:16:21
Layman speak	Juggler	2004-10-24 16:50:09
OwL seems have it	CeeAnne	2004-10-24 16:20:50
Maybe Solution	owl	2004-10-24 15:58:03
re: A quick guess	Tristan	2004-10-24 15:36:47
A quick guess	SteveH	2004-10-24 14:53:23

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