MathDB

Let

C_1

and

C_2

be circles in the same plane,

P_1

and

P_2

arbitrary points on

C_1

and

C_2

respectively, and

Q

the midpoint of segment

P_1P_2.

Find the locus of points

Q

P_1

and

P_2

go through all possible positions. Alternative version. Let

C_1, C_2, C_3

be three circles in the same plane. Find the locus of the centroid of triangle

P_1P_2P_3

P_1, P_2,

and

P_3

go through all possible positions on

C_1, C_2

, and

C_3

respectively.

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