MathDB

A segment

AB

is given and it's midpoint

K

. On the perpendicular line to

AB

, passing through

K

a point

C

, different from

K

is chosen. Let

N

be the intersection of

AC

and the line passing through

B

and the midpoint of

CK

. Let

U

be the intersection point of

AB

and the line passing through

C

and

L

, the midpoint of

BN

. Prove that the ratio of the areas of the triangles

CNL

and

BUL

, is independent of the choice of the point

C

Problem Statement