2000 AIME I Problems/Problem 12

Problem

A sphere is inscribed in the tetrahedron whose vertices are $\mathrm {A}=(6,0,0)$ , $\mathrm {B}=(0,4,0)$ , $\mathrm {C}=(0,0,2)$ , and $\mathrm {D}=(0,0,0)$ . The radius of the sphere is $\dfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

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2000 AIME I Problems/Problem 12

Problem

Solution

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