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 $P\equiv \left(x_1,y_1\right),Q\equiv \left(x_2,y_2\right);R\equiv \left(x_3,y_3\right)$, where $x_i,y_i$ (i = 1, 2, 3) are rational numbers. 

Now, the centroid of $∆$PQR is

$\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$

which 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 $P\left(0,1\right)$ and $Q\left(1,0\right);PQ=\sqrt{2}$