Let A and B be two fixed points on a given circle
and M and N the ends of any diameter. Find the locus
of the point of intersection of lines AM and BN
as MN rotates about the center of the circle.
Explore: Click here for a GSP sketch.
Prove or disprove: The locus the point of intersection of AM and BM is a circle when AB is 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 places at (near)
the ends of a diameter?