1st ASU 1961 problems Problem 6 (a) A and B move clockwise with equal angular speed along circles center P and Q respectively. C moves continuously so that AB=BC=CA. Establish C's locus and speed. *(b) ABC is an equilateral triangle and P satisfies AP=2, BP=3. Establish the maximum possible value of CP. Solution (a) Represent A, B as complex numbers z 1 + w 1 e it , z 2 + w 2 e it . Then C is (z 1 + w 1 e it ) + (z 2 + w 2 e it - z 1 - w 1 e it ) e i π/3 , which is also of the form z + w e it . However, there is one subtlety. There are actually two circles possible for C depending on which side of AB we place it. The continuity requirement means that C is normally confined to one of the circles. However, if A and B ever coincide then C may be able to switch to the other circle. If we regard "moves continuously" as allowing a discontinuous velocity, then a switch is always possible (provided A and B coincide). (b)