MathDB

Consider a rectangle

ABCD

with

AB = 2

and

BC = \sqrt3

. The point

M

lies on the side

AD

so that

MD = 2 AM

and the point

N

is the midpoint of the segment

AB

. On the plane of the rectangle rises the perpendicular MP and we choose the point

Q

on the segment

MP

such that the measure of the angle between the planes

(MPC)

and

(NPC)

shall be

45^o

, and the measure of the angle between the planes

(MPC)

and

(QNC)

shall be

60^o

.
a) Show that the lines

DN

and

CM

are perpendicular.
b) Show that the point

Q

is the midpoint of the segment

MP

Problem Statement