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Two circles intersect at $A$ and $B$. $C$ and $D$ are points on one circle and they can be moved around the circle. The line $CA$ meets the second circle in $E$. The line $DB$ meets the second circle in $F$.

As $C$ and $D$ move around one circle what do you notice about the line segments $CD$ and $EF$?

Prove your assertion.

 

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