What is the locus of the midpoint of a line segment of varying length where each end of the segment moves around a circle?
Basically speaking if you have two circles, A and B, of any radii and a point on each of the two circles C, and D then the locus of all points M the midpoint of line CD is an annulus with the center being the midpoint of the line connecting the centers. How would I prove this statement? I know the maximum and minimum distance the midpoint can be: (r1+r2)/2 and (r1-r2)/2, respectively. All I have to do is show that for any given point M in the annulus that two points C and D exist such that M is the midpoint of CD. Can you please help? Here is a link to help visualize the problem: Locus of Midpoint of Line joining Two Circles Press animate to begin the animation. Thank you for taking the time to read this and 10 points for best answer!!!
No the actual question is (sorry if I didn't make it clear) If you picked a point M within the annulus region how would construct point C on circle A and point D on circle B such that M is the midpoint of line CD? It has nothing to do with rates (again I am sorry if I didn't make that clear).
12 minutes ago