MathDB

Consider the cube

ABCDEFGH

and denote by, respectively,

M

and

N

the midpoints of

[AB]

and

[CD]

. Let

P

be a point on the line defined by

[AE]

and

Q

the point of intersection of the lines defined by

[PM]

and

[BF]

. Prove that the triangle

[PQN]

is isosceles. https://cdn.artofproblemsolving.com/attachments/0/0/57559efbad87903d087c738df279b055b4aefd.png

Problem Statement