RU-ALLRUSSIAN 1961 Problem 6

(a) A and B move clockwise with equal angular speed along circles center P and Q respectively. C moves continuously so that $\mathrm{AB = BC = CA}$ . Establish C's locus and speed. $\ast (\mathrm{b})$ ABC is an equilateral triangle and P satisfies $\mathrm{AP} = 2$ , $\mathrm{BP} = 3$ . Establish the maximum possible value of CP.