Statement 1 : If the vertices of a triangle are having rational coordinates, then its centroid, circumcenter, and orthocentre are rational. Statement 2 : In any triangle, orthocentre, centroid,and circumcenter are collinear, and the centroid divides the line joining the orthocentre and circumcenter in the ratio 2:1.

Find the centroid of the triangle whose orthocentre is (-3,5) and circumcentre is (6,2).

p : If a triangle is equilateral then its centroid, circumcenter and incentre lies at same point Converse of statement p is

Statement 1: The vertices of a triangle are (1,2), (2,1) and {1/2(3+sqrt(3)),1/3(3+sqrt(3))} Its distance between its orthocentre and circumcentre is zero. Statement 2 : In an equilateral triangle, orthocentre and circumcentre coincide.

The vertices of a triangle are (0,3) ,(-3,0) and (3,0) . The coordinates of its orthocentre are

Statement I : If centroid and circumcentre of a triangle are known its orthocentre can be found Statement II : Centroid, orthocentre and circumcentre of a triangle are collinear.

The vertices of a triangle are (0, 3), (-3, 0) and (3, 0). The coordinates of its orthocentre are

In any triangle ABC ,the distance of the orthocentre from the vertices A, B,C are in the ratio

A(-1, 3), B(4, 2) and C(3, -2) are the vertices of a triangle. Find the coordinates of the centroid G of the triangle.

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.

Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation 5x-3y=0 Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio 1:2