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Prove that the points (2 a, 4 a), (2 a, 6 a) and (2a + √3, 5a) are the vertices of an equilateral triangle.

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Let A(2 a, 4 a), B(2 a, 6 a) and C(2a + √3, 5a) be the given points

Since, AB=BC=AC

Therefore, ABC is an equilateral triangle

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AB = BC = CA 
∴ the vertices are of an equilateral triangle.    

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