A little more of a hint
- Using the Law of Cosines, from triangle ABC we get
- Note that angle AFC and angle ABC subtend the same chord (AC). Therefore they are equal. Likewise angle BFC and angle BAC subtend the same chord (BC) and therefore they are equal. That is, the measure of Angle AFB is the same as the measure of Angle A plus the measure of Angle B. Now, (angle measures) A+B = 180 - C.
- Using the Law of Cosines, from triangle AFB, we get
- or
- But cos (180 - C) = - cos(C), so
- Now, solve for n in terms of c and substitute.