MathDB

Regular octahedron - equal angles

Source: Austrian Federal Competition 2013, part 2, problem 6

June 18, 2013

geometry3D geometryoctahedronspheregeometry proposed

Problem Statement

Consider a regular octahedron

ABCDEF

with lower vertex

E

, upper vertex

F

, middle cross-section

ABCD

, midpoint

M

and circumscribed sphere

k

. Further, let

X

be an arbitrary point inside the face

ABF

. Let the line

EX

intersect

k

E

and

Z

, and the plane

ABCD

Y

. Show that

\sphericalangle{EMZ}=\sphericalangle{EYF}