Stage: 5 Challenge Level: 
In the diagram, $A$ and $B$ are fixed points on a circle, while $PQ$ is a variable diameter.
You can move the points $P$ and $Q$ in the diagram.
What is the locus of $X$ (at the intersection of $AQ$ and $BP$)?
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NOTES AND BACKGROUND
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Summation of series. Interactivities. Dynamic geometry. Making and proving conjectures. Generalising. Circle theorems. Recurrence relations. Mathematical reasoning & proof. Fibonacci sequence. Mathematical induction.
Published March 1999.
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email: nrich@damtp.cam.ac.uk
