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The circle on the line becoming a member of the inner and external centres of similitude as diameter is named the "circle of similitude." It could be proven to be the locus of the vertex of the triangle which has for its base the gap between the centres of the circles and the ratio of the remaining sides equal to the ratio of the radii of the 2 circles. Very early in the history of geometry it was known that the circumference and area of a circle of radius r may be expressed in the types 2π