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radius of a circumsphere

Source: China Second Round Test1

January 30, 2012
analytic geometrytrigonometrygeometry3D geometrytetrahedrongeometry unsolved

Problem Statement

In a tetrahedral ABCDABCD, given that ∠ADB=∠BDC=∠CDA=π3\angle ADB=\angle BDC =\angle CDA=\frac{\pi}{3}, AD=BD=3AD=BD=3, and CD=2CD=2. Find the radius of the circumsphere of ABCDABCD.
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