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angle between planes wanted, regular quadrilateral prism related

Source: 2009 Romania District VIII P3

May 19, 2020
geometry3D geometryprismplanesangle

Problem Statement

Consider the regular quadrilateral prism ABCDA′B′C′D′ABCDA'B'C 'D', in which AB=a,AA′=a22AB = a,AA' = \frac{a \sqrt {2}}{2}, and MM is the midpoint of B′C′B' C'. Let FF be the foot of the perpendicular from BB on line MCMC, Let determine the measure of the angle between the planes (BDF)(BDF) and (HBS)(HBS).
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