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kropki game

Find the image of the circle under the homothety with center O and ratio k=-1/3. On the circle mark any point A. Draw rays from points A, S through point O. Find with compass point S' that line segment OS' is three times smaller as OS. The ratio k is negative then S' is on different side of the point O. In the same way find point A'. Draw the circle with center S' and passes through the point A'. We get the circle under the homothety with center S and ratio k = -1/3.