MathDB

(040) O2

Part of 1983 Tournament Of Towns

Problems(1)

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

Source:

8/18/2019
On sides AB,BCAB, BC and CACA of triangle ABCABC are located points P,MP, M and KK, respectively, so that AM,BKAM, BK and CPCP intersect in one point and the sum of the vectors AM→,BK→\overrightarrow{AM}, \overrightarrow{BK} and CP→\overrightarrow{CP} equals 0→ \overrightarrow{0}. Prove that K,MK, M and PP are midpoints of the sides of triangle ABCABC on which they are located.
vectormedianmidpointgeometry