1. The problem statement, all variables and given/known data Hi, Refer to: http://press.princeton.edu/books/maor/chapter_7.pdf [Broken] ( Page 2 & 3) How do we derive the x-coordinate to be (R-r)cosθ + r cos[(R-r)/r]θ 2. Relevant equations Let 'r' & 'R' be radius of small & big circles respectively; Let the angle by which a point on the small circle rotates about its center, C be β 3. The attempt at a solution x-coordinate of point P relative to O = (R-r)cosθ + r cosβ = ???? The text states that the arcs of the fixed & moving circles that come into contact must be of EQUAL LENGTH. May I know how do we prove it mathematically?