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Find the volume of the tetrahedron

Source: Vietnam NMO 1962 Problem 4

February 1, 2009
geometry3D geometrytetrahedrongeometry unsolved

Problem Statement

Let be given a tetrahedron ABCD ABCD such that triangle BCD BCD equilateral and AB \equal{} AC \equal{} AD. The height is h h and the angle between two planes ABC ABC and BCD BCD is α \alpha. The point X X is taken on AB AB such that the plane XCD XCD is perpendicular to AB AB. Find the volume of the tetrahedron XBCD XBCD.
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