The medians AD, BE and CF in ΔABC pass through point G.

(a) If GF = 4 cm then find the value of GC.

(b) If AD = 7.5 cm then find the value of GD.

Given that in ∆ABC, medians AD, BE and CF intersects at a point G.

GF = 4 cm and AD=7.5 cm

As we know that if the medians in a triangle intersect at a point then the point is the centroid of the triangle and the centroid divides the median in 2:1 ratio.

Here, G is the centroid of the ∆ABC.

And AG:GD = 2:1,

BG:GE = 2:1 ,

CG:GF = 2:1

Now, AD=AG+GD

⇒AG=2GD………….(1)

AD = AG+GD………………(1)

⇒AG=2GD

Putting in equation (1)

7.5 = 2GD+GD

⇒ 3GD=7.5

⇒ GD = 2.5

GD = 2.5 cm

Again,

⇒ CG=4×2=8

CG=8 cm

Hence, GD=2.5 cm, and CG=8 cm