Consider a (right) square pyramid ABCDV with the apex V and the base (square) ABCD. Denote d=AB/2 and φ the dihedral angle between planes VAD and ABC.
(1) Consider a line XY connecting the skew lines VA and BC, where X lies on line VA and Y lies on line BC. Describe a construction of line XY such that the segment XY is of the smallest possible length. Compute the length of segment XY in terms of d,φ.
(2) Compute the distance v between points V and X in terms of d,φ. geometrycomputational geometryconstructive geometry3D geometrypyramidnational olympiad