Let

AandBbe two fixed points on a given circle andMandNthe ends of any diameter. Find the locus of the point of intersection of linesAMandBNasMNrotates about the center of the circle.

Explore: Clickherefor a GSP sketch.

Prove or disprove: The locus the point of intersection ofAMandBMis a circle whenABis a chord that is not a diameter.

Question: Where is the center of the circle and what is its radius?

Extension: What happens as A and B are placed at (near) the ends of a diameter?

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