smallest sphere

Geometry Level 3

The radius of smallest sphere which passes through the points $(1,0,0) (0,1,0)$ and $(0,0,1)$ has radius given by $\sqrt { \frac { a }{ b } }$ where $a$ and $b$ are coprime to each other. then $a+b$ is equal to?

The answer is 5.

1 solution

Saya Suka
Dec 7, 2016

The equilateral triangle with vertices (1,0,0) , (0,1,0) and (0,0,1) would have to be inscribed inside the largest circle on the sphere that we are looking for. So for the equal side of √2, the radius of sphere equal the radius of its hemispherical circle, at √(2/3). Answer = 2+3=5.

smallest sphere

The answer is 5.

1 solution

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