MathDB

In the cuboid

ABCDA'B'C'D'

with

AB=a

AD=b

and

AA'=c

such that

a>b>c>0

, the points

E

and

F

are the orthogonal projections of

A

on the lines

A'D

and

A'B

, respectively, and the points

M

and

N

are the orthogonal projections of

C

on the lines

C'D

and

C'B

, respectively. Let

DF\cap BE=\{G\}

and

DN\cap BM=\{P\}

.
[*] Show that

(A'AG)\parallel (C'CP)

and determine the distance between these two planes; [*] Show that

GP\parallel (ABC)

and determine the distance between the line

GP

and the plane

(ABC)

.
Petre Simion, Nicolae Victor Ioan

Problem Statement