Mathematics

Mathematics

Problem

Two pulleys of radii 2 m2\,\text{m} and 3 m3\,\text{m} have their centers 13 m13\,\text{m} apart. A belt connects them, crossing between the pulleys (an internal tangent). The line of the belt meets the line joining the centers at a specific point. If we consider the pulleys as circles in a Cartesian plane with the first center at origin (0,0)(0,0) and the second at (13,0)(13,0), find the coordinates of this intersection point, which is also the center of similitude for internal tangency.

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