Let C1 and C2​ be circles with centres 10 units apart, with radii of length 1 and 3 respectively. Firstly find the locus of all points, M, for which there exist points X on C1 and Y on C2 such that M is the midpoint of the line segment XY. Then find the area of the closed region inscribed by the locus.

From the definition of a midpoint, the midpoint is equidistant from both endpoints. In addition, each point on a perpendicular bisector of this segment has the same distance between each endpoint (which is not the same distance as the other points on the perpendicular bisector). So, the perpendicular bisector of a line segment is its locus.

Posted by Sara Fritz on 2021-02-18 06:45:58