I have been trying to solve this problem and am stumped. Diagram below. My approach has been trying to show that $\Delta VKM$ is isosceles, since the bisector of the unequal angle of an isosceles triangle is perpendicular to the opposite side (which in this case is the bisector at W). I have gone down various blind alleys attempting to show that $\angle LKV = \angle LMV,$ many of them involving a line l through V and parallel to t (not shown, since I think this is the wrong approach). Although this gets me annoyingly close to my goal, I always wind up subtly assuming something that implies what I am trying to prove (for example that a perpendicular to l, t is parallel to s). The hint just says to compare the arcs into which the circle is divided by the bisectors at V and W, but I am not seeing it.
This is problem 3.2.8 in Coxeter and Greitzer's Geometry Revisited. Thanks for any help, I would really appreciate it.