Given a line, two points, and a circle. Draw a circle that passes through the points and whose chord with the given circle is parallel to the given line.
The geometric place of one of the perpendiculars dropped from the center of the given circle to the given line is the center of the sought circle; the second geometric place is obtained by erecting a perpendicular at the midpoint of the line segment connecting the given points.

(Osztián Kálmán, Szamosujvár.)

Number of solutions: 27.