MathDB

We color some points in the plane with red, in such way that if

P,Q

are red and

X

is a point such that triangle

\triangle PQX

has angles

30º, 60º, 90º

in some order, then

X

is also red. If we have vertices

A, B, C

all red, prove that the barycenter of triangle

\triangle ABC

is also red.

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