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'Bi-cyclics' printed from http://nrich.maths.org/
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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