(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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