Solve this: 40 P, Q and R are on ML, NL and MN of the equilateral triangle - Maths - Circles

Question

Solve this:

40 P, Q and R are on ML, NL and MN of the equilateral
triangle MLN respectively If MP : PL= NQ : QL = 1 : 2 and G is the
centroid of the triangle PQL and S is the mid point of MN Find LG :
GS

(A) 2 : 3 (B) 4 : 5
(C) 3 : 4 (D) 1 : 3
(E) None of these

Ankita Agarwal · Accepted Answer

Dear Student,
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a2cbe6673c46%20png">

Given : MP : PL= NQ : QL = 1 : 2and S is a mid point of MN So O become centroid of ∆MLNHence LOOS=21   
i   Property of centroid: The centroid divides each median in a ratio of 2:1and G is a Centroid of ∆PLQ LGGO=21
iiFrom equation iLOOS=21LG+GOGS-GO=21from eqnii GO=LG2LG+LG2GS-LG2=21LG+LG2=2GS-LG22LG+LG2=2GS-LG32LG=2GS-LG32LG+LG=2GS3LG+2LG2=2GS5LG=4GSLGGS=45Hence Option B is correct

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Solve this: 40. P, Q and R are on ML, NL and MN of the equilateral triangle MLN respectively. If MP : PL= NQ : QL = 1 : 2 and G is the centroid of the triangle PQL and S is the mid point of MN. Find LG : GS. (A) 2 : 3 (B) 4 : 5 (C) 3 : 4 (D) 1 : 3 (E) None of these

Solve this:

40. P, Q and R are on ML, NL and MN of the equilateral triangle MLN respectively. If MP : PL= NQ : QL = 1 : 2 and G is the centroid of the triangle PQL and S is the mid point of MN. Find LG : GS.

(A) 2 : 3 (B) 4 : 5
(C) 3 : 4 (D) 1 : 3
(E) None of these