MathDB

A semicircle

S

is drawn on

AB

as diameter. For an arbitrary point

C

S

(

C\ne A

C \ne B

), squares are attached to sides

AC

and

BC

of triangle

ABC

outside the triangle. Find the locus of the midpoint of the segment joining the centres of the squares as

C

moves along

S

.
(J Tabov, Sofia)

Problem Statement