Question

7. Fill in the blanks.
their points of coll
R
Point G is the centroid of A ABC.
(1) If I(RG) = 2.5 then I(GC) =
(2) If I(BG) = 6 then I(BQ) =
(3) If I(AP) = 6 then I(AG) =
с and I(GP) =
G
B
P
pzzz give answer
123 pzzzzzzzzzzz​

Answer 1

In ∆ABC, the medians AP, BQ and CR to the sides BC, CA and AB respectively intersect at G. Since, centroid of a triangle divides the medians in the ratio of 2 : 1, then AG : GP = BG : GQ = CG : GR = 2 : 1.

(1) We have, CG : GR = 2 : 1

⇒GCRG=21⇒GC2.5=21⇒GC=5

(2) We have, BG : GQ = 2 : 1

⇒BGGQ=21⇒BGBQ−BG=21⇒6BQ−6=2⇒BQ−6=3⇒BQ=9

(3) We have, AG : GP = 2 : 1

⇒AGGP=21⇒AGAP−AG=2⇒AG6−AG=2⇒2(6−AG)=AG⇒12−2AG=AG⇒3AG=12⇒AG=123⇒AG=4

Now, GP = AP − AG = 6 − 4 = 2.

Hence, we have,

(1) If l(RG) = 2.5 then l(GC) = 5

(2) If l(BG) = 6 then l(BQ) = 9

(3) If l(AP) =6 then l(AG) = 4 and l(GP) = 2