The three marked angles at Q (circle, x and bullet) add up to 180º. Also the three angles in the triangle add up to 180º. But these angles are an x (at Q), a circle plus a star (at ) and a bullet minus a star (at ). It follows that the two angles marked with a star ( and ) must be equal. By the "angles on the same segment" theorem, or rather its converse, it follows that the points lie on a circle.
[It then follows fairly easily from this that the points are collinear.]