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TOT 040 1983 Spring S-O2 S-A2 median vector sum proof, reverse

Source:

August 18, 2019

vectormedianmidpointgeometry

Problem Statement

On sides

AB, BC

and

CA

of triangle

ABC

are located points

P, M

and

K

, respectively, so that

AM, BK

and

CP

intersect in one point and the sum of the vectors

\overrightarrow{AM}, \overrightarrow{BK}

and

\overrightarrow{CP}

equals

\overrightarrow{0}

. Prove that

K, M

and

P

are midpoints of the sides of triangle

ABC

on which they are located.

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