Two medians BE and CF of `Delta ABC` intersect at G. Prove that area of the quadrilateral `AFGE=(1)/(3)Delta ABC.`

In a Delta ABC

(ix) AD, BE and CF are the three medians of Delta ABC and intersect at G. The area of the Delta ABC is 36 Sq. cm. Find (a) the area of Delta AGB and (b) the area of the quadrilateral BDGF.

The medians BE and CF of the DeltaABC intersect each other at G and the line segment EF intersects AG at O. Prove that OA = 3.OG.

E is the mid-point of AD , a median of the Delta ABC . The extended BE intersects AC at F. prove that AF=(1)/(3)AC.

P is a point on the median AD of the Delta ABC . Prove that area of Delta APB = area of Delta APC .

In Delta ABC,AB= AC and E is any point on the extended BC. The circumeircel of Delta ABC intersects AE at the point D. Prove that angle ACD= angle AEC .

D, E, F are mid points of sides BC, CA, AB of Delta ABC . Find the ratio of areas of Delta DEF and Delta ABC .

G is the centroid of triangle ABC and A_1 and B_1 are the midpoints of sides AB and AC , respectively. If Delta_1 is the area of quadrilateral G A_1A B_1 and Delta is the area of triangle ABC , then Delta/Delta_1 is equal to a. 3/2 b. 3 c. 1/3 d. none of these

If in triangle ABC cosA+cosB+cosC=3/2 then prove that triangle is equilateral