MathDB

dihedral angle between the planes $(MA_1C)$ and $(NA_1C)$

Source: Moldova TST 1996

August 8, 2023

geometry3D geometry

Problem Statement

Let

ABCDA_1B_1C_1D_1

be a cube. On the sides

AB{}

and

AD{}

there are the points

M{}

and

N{}

, respectively, such that

AM+AN=AB

. Show that the measure of the dihedral angle between the planes

(MA_1C)

and

(NA_1C)

doe not depend on the positions of

M{}

and

N{}

. Find this measure.