2001 AIME I Problems/Problem 12
Problem
A sphere is inscribed in the tetrahedron whose vertices are 
and 
The radius of the sphere is 
where 
and 
are relatively prime positive integers. Find 
Solution
![[asy]import three; pointpen = black; pathpen = black+linewidth(0.7); currentprojection = perspective(5,-10,4); triple A = (6,0,0), B = (0,4,0), C = (0,0,2), D = (0,0,0); triple I = (3/2,1,1/2); draw(C--A--D--C--B--D--I--A--B--I--C); label("$I$",I,S); label("$A$",A,S); label("$B$",B,E); label("$C$",C,N); label("$D$",D,W);[/asy]](http://latex.artofproblemsolving.com/d/7/c/d7cfeed8b9d8a63a7d63621747ffb9d2cb2ee98a.png)
See also
- <url>viewtopic.php?p=384205#384205 Discussion on AoPS</url>
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