AB and CD-diameters of one circle. Prove that AC is parallel to BD and find the angle ABC if the angle BD = 44 degrees.

In triangles AOC and BOD, the angle AOC = BOD as vertical angles when crossing the diameters AB and CD, OC = OA = OB = OD as the radii of a circle, then triangles AOC and BOD are equal on two sides and the angle between them.

Then the angle ОАС = ОВD, and since these are criss-crossing angles at the intersection of straight lines АС and ВD secant AB, then АС is parallel to ВD, which was required to be proved.

Similarly, the triangles AOD and BOC are equal, then the angle BAD = ABC = 44.

Answer: Angle ABC is 44.