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Definition of a circle

If a, b, c are in A.P., a, x, b are in G.P. and b, y, c are in G.P., the point (x, y) lies on


We have 2b = a +c , x2= ab, y2 = bc.

so that x2+y2= b(a +c) = 2b2 which is a circle.

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