44. (8th grade) Given a circle and a point $A$ outside it. Find the geometric locus of the midpoints of the chords whose extensions pass through the point $A$.
44. We draw a series of secants from point A and mark the midpoints of the obtained chords. By connecting the midpoints of the chords with the center of the given circle O, we obtain a series of right triangles: \( O A B_{1}, O A B_{2}, O A B_{3}, O A B_{4} \) and so on. The midpoints of the chords form a circle, the diameter of which is the segment \( O A \).