Show that four skew lines in $\mathbb{P}^3$ have two transversals in common.

I know that exist a quadric which contains three of the four lines....but i'm stuck


If the skew lines are $a,b,c,d$. Let $Q$ the quadric such that $a,b,c \subset Q$. Then $d \cap Q=\text{{two point}}$? Why?


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