I have attempted drawing this many times and cannot come up with a cardioid. I believe the AM1 and AM2 are what is confusing me. I honestly have no idea where to start in order to find the equation. This is the first assignment of my Differential Geometry course and its been many years since I have taken calc 3. Any direction would be greatly appreciated.
Question:
Let O be a point on a circle of radius a, and a ray intersecting the circle at a varying point A rotates around O. Mark off two line segments AM1=AM2=2a on this ray on two sides of A. Deduce the equation of a curve traced by the points M1 and M2.