the question is misleading....
simple question on same chords and their same distance to centre of circle.
OPXQ has 3 right angles, and then PX = QX, PO = QO, so it can only be a square.
If your diagram is correct, then the question is not misleading - it's just plain wrong. Nothing is subtending an angle of at . And how do you know that is the point of intersection of the chords? They are described as and , not and .