MathDB

IOQM 2023-24 P-14

Source:

September 3, 2023

geometrycoordinate geometryMediansCentroidIOQM

Problem Statement

Let

A B C

be a triangle in the

x y

plane, where

B

is at the origin

(0,0)

. Let

B C

be produced to

D

such that

B C: C D=1: 1, C A

be produced to

E

such that

C A: A E=1: 2

and

A B

be produced to

F

such that

A B: B F=1: 3

. Let

G(32,24)

be the centroid of the triangle

A B C

and

K

be the centroid of the triangle

D E F

. Find the length

G K

.

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