MathDB

ABCDA'B'CD'

is a rectangular parallelepiped with

AA'= 2AB = 8a

E

is the midpoint of

(AB)

and

M

is the point of

(DD')

for which

DM = a \left( 1 + \frac{AD}{AC}\right)

.
a) Find the position of the point.

F

on the segment

(AA')

for which the sum

CF + FM

has the minimum possible value.
b) Taking

F

as above, compute the measure of the angle of the planes

(D, E, F)

and

(D, B', C')

.
c) Knowing that the straight lines

AC'

and

FD

are perpendicular, compute the volume of the parallelepiped

ABCDA'B'C'D'

Problem Statement