G is the centroid of the triangle ABC. Prove that the area of the triangle ABG is one third of the area of the triangle ABC.

The point H orthocentre of the triangle ABC. A point K is taken on the straight line CH such that ABK is a right triangle. Prove that the area of the triangle ABK is the geometric mean between the area of the triangles ABC and ABH.

The medians of a triangle ABC meet at G. If the area of the triangle be 120 sq cm, then the area of the triangle GBC is

The centroid of a triangle ABC is G. The area of triangle ABC is 60 cm^(2) . The area of triangle GBC is.

In Fig. 9.29 ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD.

Consider the following statements : 1. Let D be a point on the side BC of a triangle ABC: If area of triangle ABD = area of triangle ACD, then for all points O on AD, area of triangle ABO = area of triangle ACO. 2. If G is the point of concurrence of the medians of a triangle ABC, then area of triangle ABG = area of triangle BCO = area of triangle ACG. Which of the above statements is/are correct?

X is a point on median AL of triangle ABC. Prove that triangle ABX is equal in area.

If G is the centroid of Delta ABC , then the area of Delta BGC is "_______________" times the area of quadrilateral ABCG.