通过$(0,l_i)(1,r_i)$的直线

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$P_i(l_i,r_i),i=1,2,3$为任意点, $L_i$为通过$(0,l_i)(1,r_i)$的直线, $Q_{i,k}$为$L_i,L_k$的交点, 过$Q_{i,k}$作$y$轴平行线交$L_j$于点$Q_{i,k|j}$, 则$$Q_{1,2}Q_{1,2|3}\cdot Q_{2,3}Q_{2,3|1}\cdot Q_{3,1}Q_{3,1|2}=4\S{P_1P_2P_3}\S{Q_{1,2}Q_{2,3}Q_{3,1}}$$

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过$Q_{1,2},Q_{2,3},Q_{3,1}$的二次函数的二次项系数为$\dfrac{\S{P_1P_2P_3}}{\S{Q_{1,2}Q_{2,3}Q_{3,1}}}$