State Apollonius Theorem and Centroid divides circumcentre and orthocentre in 1:2

State Apollonius Theorem and Centroid divides median in the ratio 2:1?

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 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 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.

(1) If coordinates of centroid and circumcentre of a triangle are known, coordinates of its orthocentre can be obtained. (2) Centroid, circumcentre and orthocentre of a triangle are collinear. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

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.

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.

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