If a triangle has it's orthocenter at (1,1) and circumcentre (3/2,3/4) then centroid is:

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

In an equilateral triangle, prove that centroid and circumcentre coincide.

The area of a triangle with vertices at (-4,-1), (1,2) and (4,-3) is:

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

The vertices of a triangle are (1, a), (2, b) and (c^(2)-3) Find the condition that the centroid may lie on the X-axis.

Two vertices of a traingle are (2,-6,4) and (4,-2,3) and its centroid is (8/3,-1,3) . Find the third vertex.

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.