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angle of intersection of planes

Source: Ukraine 1999 Grade 11 P3

May 11, 2021
3D geometrygeometry

Problem Statement

All faces of a parallelepiped ABCDA1B1C1D1ABCDA_1B_1C_1D_1 are rhombi, and their angles at AA are all equal to α\alpha. Points M,N,P,QM,N,P,Q are selected on the edges A1B1,DC,BC,A1D1A_1B_1,DC,BC,A_1D_1, respectively, such that A1M=BPA_1M=BP and DN=A1QDN=A_1Q. Find the angle between the intersection lines of the plane A1BDA_1BD with the planes AMNAMN and APQAPQ.
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