A Collinearity Involving an Excircle, the Incircle, and the Circumcircle

Let ABC be a triangle with incenter I and circumcircle . Let J be the excenter of the excircle opposite A. Let IJ intersect BC at D and let IJ intersect at M. Let N be the midpoint of arc MBA of . Let S and T be the second intersection points of NI, NJ with . Then S, D, T are collinear.