5.2.4.42 Various problems on the plane

Condition: The bisectors of the external angles at the vertices \( A \) and B of the triangle \( A B C \) intersect at the point \( J \), and \( A J=B J \). Find \( A C \) if \( \angle A B C=\beta \), and the radius of the circle circumscribed by the triangle \( A B C \) is equal to \( R \).