Where the angle bisectors intersect determines the center of the incircle. Where the side perpendicular bisectors intersect determines the center of the center of the circumcircle. From these definitions, you should be able to determine the points you want.
See, pls, the suggested explanation: S - the centre of inscribed circle, P - the centre of circumscribed circle. Details are in the attached picture: red lines for small circle (inscribed), green ones for large (circumscribed).
