Question: In triangle ABC, angle A = 60°, AC = 21, BC = 19. The circle inscribed in triangle ABC touches the sides AB, BC, and CA at points P, Q, R respectively. Find all possible lengths of all AB, BQ and the radius of the inscribed circle.
Using the sine law, I have found that angle $B = 73.17355^\circ$ and angle $C = 46.82645^\circ$. I also found that the missing side length $C$ is $16$.
However, I don't understand how I can somehow use this knowledge to find the radius of the circle inscribed within the triangle. In addition, how can there be more than one length for $AB$ and $BQ$?