Suppose you have two circles, one with radius r1 centered at the origin, and one with radius r2 centered at (r1 + r2 ; 0). Thus, the circles have the point P = (r1 ; 0) in common. Suppose the circle with radius r2 begins rolling counterclockwise along the outside of the other circle. As the circle rotates, the point that was originally at P will also rotate, tracing out a path in the plane. Find parametric equations for this path. Anybody that gets this right I will fan and medal!

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Suppose you have two circles, one with radius r1 centered at the origin, and one with radius r2 centered at (r1 + r2 ; 0). Thus, the circles have the point P = (r1 ; 0) in common. Suppose the circle with radius r2 begins rolling counterclockwise along the outside of the other circle. As the circle rotates, the point that was originally at P will also rotate, tracing out a path in the plane. Find parametric equations for this path. Anybody that gets this right I will fan and medal!

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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