Locus of the Intersection of Two Secants

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 placed at (near) the ends of a diameter?

Return to the EMAT 4600/6600 Page