Equilateral triangle
Construct an equilateral triangle with two vertices on the given circle and two sides passing thru the given points.
Hint:
Construct a circle Г containing points from which the given points are seen at an angle of π/3; it must contain the third vertex. Observe that the angle bisector at the third vertex passes thru the center of the big circle and the midpoint of the arc of Г between the given two points.