Try exploring the intersecting chords a little using the interactive diagram found at the link below.

Here, two intersecting chords are drawn, along with their perpendicular bisectors. Remember that the perpendicular bisector of ANY chord always goes through the center of the circle.

https://www.geogebra.org/classic/txtevd2v

You should be able to drag points A, B, C, and D around the circle, try to do so to match the angles in the problem if needed.