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Tetrahedron

Source: 2003 National High School Mathematics League, Exam One, Problem 6

March 16, 2020
geometry3D geometrytetrahedron

Problem Statement

In tetrahedron ABCDABCD, AB=1,CD=3AB=1,CD=3, the distance between ABAB and CDCD is 22, the intersection angle between ABAB and CDCD is π3\frac{\pi}{3}, then the volume of tetrahedron ABCDABCD is (A)32(B)12(C)13(D)33\text{(A)}\frac{\sqrt3}{2}\qquad\text{(B)}\frac{1}{2}\qquad\text{(C)}\frac{1}{3}\qquad\text{(D)}\frac{\sqrt3}{3}
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