5.2.4.25 Various problems on the plane

In a regular triangle \( A B C \) with side 12, a semicircle is constructed on the side \( B C \) as a diameter, which has no common points with the triangle \( A B C \), except for the points \( B \) and \( C \). It is divided by the points \( A_{1} \) and \( A_{2} \) into three equal arcs \( B A_{1}=A_{1} A_{2}=A_{2} C \). Find the lengths of the segments into which the side \( B C \) is divided by the straight lines \( A A_{1} \) and \( A A_{2} \).