If the vertices P, Q, R of a ∆PQR are rational points, which of the following points of the ∆PQR is (are) always rational point(s)?

Let P≡x1,y1,Q≡x2,y2;R≡x3,y3, where xi,yi (i = 1, 2, 3) are rational numbers. Now, the centroid of ∆PQR isx1+x2+x33,y1+y2+y33which is rational point. Incentre, circumcentre and orthocentre depend on sides of the triangle which may not be rational even if vertices are so. For example, for P0,1 and Q1,0;PQ=2