6. As shown in Figure $2, \odot O_{1}$ and $\odot O_{2}$ intersect at points $E$ and $F$, $AB$ and $CD$ are two common tangents, line $EF$ intersects $AB$ and $CD$ at points $P$ and $Q$ respectively. The relationship between $AB$, $PQ$, and $EF$ is ( ).
(A) $2 AB=PQ+EF$
(B) $AB^2=PQ \cdot EF$
(C) $AB^2+EF^2=PQ^2$
(D) $\frac{1}{EF}=\frac{1}{PQ}+\frac{1}{AB}$
6.C.

Let $P E=Q F=a, E F=b$. Then $P Q^{2}=(2 a+b)^{2}=4 a^{2}+4 a b+b^{2}$.
And $A B^{2}=4 P A^{2}=4 P E \cdot P F$
$$
=4 a(a+b)=4 a^{2}+4 a b \text {, }
$$

Thus $A B^{2}+E F^{2}=4 a^{2}+4 a b+b^{2}=P Q^{2}$.