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let vectors a , b, c represent A,B,C respectively
so mid point vecors of D,E,F respectively are 1/2*(b+c) , 1/2*(a+c) , 1/2*(b+a)
AD+BE+CF = 1/2*(b+c) - a + 1/2*(a+c) -b + 1/2*(b+a) - c
AD+BE+CF = 0
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