MathDB

Consider the cube

ABCDA'B'C'D'

. The bisectors of the angles

\angle A' C'A

and

\angle A' AC'

intersect

AA'

and

A'C

in the points

P

, respectively

S

. The point

M

is the foot of the perpendicular from

A'

CP

, and

N

is the foot of the perpendicular from

A'

AS

. Point

O

is the center of the face

ABB'A'

a) Prove that the planes

(MNO)

and

(AC'B)

are parallel.
b) Calculate the distance between these planes, knowing that

AB = 1

Problem Statement