MathDB
Don Quixotetrahedron

Source: 2017 AIME II #15

March 23, 2017
AIMEAIME IAIME II

Problem Statement

Tetrahedron ABCDABCD has AD=BC=28AD=BC=28, AC=BD=44AC=BD=44, and AB=CD=52AB=CD=52. For any point XX in space, define f(X)=AX+BX+CX+DXf(X)=AX+BX+CX+DX. The least possible value of f(X)f(X) can be expressed as mnm\sqrt{n}, where mm and nn are positive integers, and nn is not divisible by the square of any prime. Find m+nm+n.
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