Three objects A,B,C are each at a vertex of an equilateral triangle of side a. At t=0, they set out towards each other such that, at any instant, A is heading towards B, B towards C and C towards A with a uniform speed v. After what time and distance will they meet? What is the equation of their path?

The path traveled by such objects are actually called logarithmic spirals. If center of the triangle is considered to be origin then in polar coordinates, the trajectory followed by one such object is given by