MathDB

Sphere

Source: AIME 2 2000 #12

December 9, 2005

geometry3D geometryspherecircumcircletrigonometrytetrahedronnumber theory

Problem Statement

The points

A, B

and

C

lie on the surface of a sphere with center

O

and radius 20. It is given that

AB=13, BC=14, CA=15,

and that the distance from

O

to triangle

ABC

is

\frac{m\sqrt{n}}k,

where

m, n,

and

k

are positive integers,

m

and

k

are relatively prime, and

n

is not divisible by the square of any prime. Find

m+n+k.

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