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

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

If the vertices of a triangle have rational coordinates, then prove that the triangle cannot be equilateral.

If the coordinates of vertices of a triangle is always rational then the triangle cannot be

Which one of the following points in the figure is the median of the points M, P, Q, R and S?

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

In the given triangle P, Q and R are the mid points of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.

Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).