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Let vertices of an acute-angled triangle...

Let vertices of an acute-angled triangle are `A(z_1),B(z_2),a n dC(z_3)dot` If the origin `O` is he orthocentre of the triangle, then prove that `z_1 bar z _2+ bar z _1z_2=z_2 bar z _3+ bar z _2z_3=z_3 bar z _1+ bar z _3z_1`

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