MathDB

Let

PQ

be a line segment of constant length

\lambda

taken on the side

BC

of a triangle

ABC

with the order

B,P,Q,C

, and let the lines through

P

and

Q

parallel to the lateral sides meet

AC

P_1

and

Q_1

and

AB

P_2

and

Q_2

respectively. Prove that the sum of the areas of the trapezoids

PQQ_1P_1

and

PQQ_2P_2

is independent of the position of

PQ

BC.

Problem Statement