If the coordinates of the vertices of a triangle an: rational numbers, then which of the following points of the triangle may not have rational coordinates?

Let Ax1,y1,Bx2,y2 and Cx3,y3vertices of △ABC such that x1,x2,x3,y1,y2,y3  are rational numbers. Then,x1+x2+x33 and y1+y2+y33 are also rational numbersSo, the coordinates of the centroid are always rational numbers.Let P be the circumcentre of .∆ABC. ThenPA=PB=PC⇒ PA2=PB2=PC2⇒ PA2=PB2 and PB2=PC2