Let ABC be a triangle whose centroid is G, orthocentre is H and circumcentre is the origin 'O'. If D is any point in the plane of the triangle such that no three of O,A,C and D are collinear satisfying the relation. AD+BD+CH+3HG= lamdaHD , then what is the value of the scalar lamda .

Find the third vertex of a triangle , if two of its vertices are at (-3,1) and (0,-2) and the centroid is at the origin.

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.

An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the coordinates of the third vertex.

If the orthocentre and centroid of a triangle are (-3, 5) and (3, 3) then its circumcentre is

If a vertex of a triangle is (1, 1) and the mid-points of two side through this vertex are (-1, 2) and (3, 2), then centroid of the triangle is

If z_(1),z_(2)andz_(3) are the vertices of an equilasteral triangle with z_(0) as its circumcentre , then changing origin to z_(0) ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.

Two vertices of a triangle are (-1, 4) and (5, 2). If its centroid is (0, -3), find the third vertex.

The hypotenuse of a right angled triangle has its ends at the points (1, 3) " and " (-4, 1) . Find an equation of the legs (perpendicular sides) of the triangle.