Question 196
Let $EFGH$, $ADC$ and $E_1F_1G_1H_1$ be three convex quadrilaterals, satisfying:
(a) Points $E$, $F$, $G$ and $H$ lie on sides $AB$, $BC$, $CD$ and $DA$, respectively, and $\frac{AE}{EB} \cdot \frac{BF}{FC} \cdot \frac{CG}{GD} \cdot \frac{DH}{HA} = 1$;
(b) points $A$, $B$, $C$ and $D$ lie on sides $H_1E_1$, $E_1F_1$, $F_1G_1$ and $G_1H_1$, respectively, and $E_1F_1 \parallel EF$, $F_1G_1 \parallel FG$, $G_1H_1 \parallel GH$, $H_1E_1 \parallel HE$.
Suppose $\frac{E_1A}{AH_1} = \lambda$, find the expression of $\frac{F_1C}{CG_1}$ in terms of $\lambda$. (posed by Xiong Bin)
(a) Points $E$, $F$, $G$ and $H$ lie on sides $AB$, $BC$, $CD$ and $DA$, respectively, and $\frac{AE}{EB} \cdot \frac{BF}{FC} \cdot \frac{CG}{GD} \cdot \frac{DH}{HA} = 1$;
(b) points $A$, $B$, $C$ and $D$ lie on sides $H_1E_1$, $E_1F_1$, $F_1G_1$ and $G_1H_1$, respectively, and $E_1F_1 \parallel EF$, $F_1G_1 \parallel FG$, $G_1H_1 \parallel GH$, $H_1E_1 \parallel HE$.
Suppose $\frac{E_1A}{AH_1} = \lambda$, find the expression of $\frac{F_1C}{CG_1}$ in terms of $\lambda$. (posed by Xiong Bin)