5.2.4.42 Various Problems on the Plane

Condition: bisectors of external angles at vertices \ (a \) and in the triangle \ (a b c \) intersect at point \ (j \), and \ (a j = b j \). Find \ (a c \) if \ (\ angle a b c = \ beta \), and the radius of the circle described near the triangle \ (a b c \) is equal to \ (r \).