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The coordinatse of the vertices A, B and...

The coordinatse of the vertices A, B and C of the triangle ABC taken in anticlockwise order are respectively `(x_r , y_r ), r = 1, 2, 3`. Prove that the angle `A` is acute or obtuse according as : `(x_1 - x_2) (x_1 - x_3) + (y_1 - y_2) (y_1 - y_3) gt 0 or lt0`.

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