Final Round

Three cyclists start from town $A$ simultaneously. They move along the closed route consisting of three straight-line segments $AB$, $BC$ and $CA$. The speeds of the first cyclist on these segments are $12$, $10$ and $15$ kilometers per hour, respectively. The speeds of the second cyclist are $15$, $15$ and $10$ (km/h) and the speeds of the third cyclist are $10$, $20$ and $12$ (km/h). Find the value of the angle $ABC$ if all three cyclists finish at town $A$ at the same time.