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Circle, Circle, Sphere! (Posted on 2004-08-26) Difficulty: 4 of 5
A circle of radius 2 is contained in the plane y=3.

A circle of radius 4 is contained in the plane y=7.

Both circles lie on the surface of a sphere.

What is the radius of the sphere?

See The Solution Submitted by SilverKnight    
Rating: 2.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re: No Subject | Comment 2 of 8 |
(In reply to No Subject by bernie)

Let one of the unknown legs be x, and the other (4-x).  Then

r^2 = 2^2 + (4-x)^2 = 4^2 + x^2

Forgetting r for the moment, and expanding:

20 - 8x + x^2 = 16 + x^2

Solving:

x=1/2

Substituting:

r^2 = 16 + 1/4

r=sqrt(16.25) or about 4.031128874149275.


  Posted by Charlie on 2004-08-26 14:32:20
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