Step 1. Find the point, D, where those two lines intersect.

Step 2. Find the distance, d(A,D). The is the circum-radius.

Step 3. Write the equations of the two lines through A each of which is perpendicular to one of the given lines

Step 4. Find the points on the lines in step 3 where the circum-circle insects.

Step 5: Those points are B & C.