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Pythagorean Pyramid (Posted on 2004-04-26) Difficulty: 3 of 5
The pictured tetrahedron has four identical rectangular (i.e., right-angled or pythagorean) triangles as faces, with

and p+q=r.

What's its volume, as a function of p, q and r?

See The Solution Submitted by Federico Kereki    
Rating: 4.1250 (8 votes)

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Solution Working with spheres | Comment 6 of 15 |
D, if it exists, is the intersection of four different spheres:

* a sphere with radius r and certer at A
* a sphere with radios q and center at B
* a sphere with radius p and cneter at C
* a sphere with diameter r and center at the midpoint of BC

It's easy to see that if D is the symmetric of A with regard to the midpoint of BC, then D satisfies all four coinditions, but it should be proved that no otherp oint also does.

  Posted by e.g. on 2004-04-26 12:25:38
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