MathDB

Let

EFGH,ABCD

and

E_1F_1G_1H_1

be three convex quadrilaterals satisfying:
i) The points

E,F,G

and

H

lie on the sides

AB,BC,CD

and

DA

respectively, and

\frac{AE}{EB}\cdot\frac{BF}{FC}\cdot \frac{CG}{GD}\cdot \frac{DH}{HA}=1

; ii) The points

A,B,C

and

D

lie on sides

H_1E_1,E_1F_1,F_1,G_1

and

G_1H_1

respectively, and

E_1F_1||EF,F_1G_1||FG,G_1H_1||GH,H_1E_1||HE

.
Suppose that

\frac{E_1A}{AH_1}=\lambda

. Find an expression for

\frac{F_1C}{CG_1}

in terms of

\lambda

.
Xiong Bin

Problem Statement