MathDB

Let

P

be a point inside a triangle

ABC

. A line through

P

parallel to

AB

meets

BC

and

CA

at points

L

and

F

, respectively. A line through

P

parallel to

BC

meets

CA

and

BA

at points

M

and

D

respectively, and a line through

P

parallel to

CA

meets

AB

and

BC

at points

N

and

E

respectively. Prove \begin{align*} [PDBL] \cdot [PECM] \cdot [PFAN]=8\cdot [PFM] \cdot [PEL] \cdot [PDN] \\ \end{align*}
Proposed by Steve Dinh

Problem Statement