We take A = A' as the origin and B = B' = any point other than A on the line intersection of π1 and π2.
Now, consider C = C' = any point niether on π1 nor π2.
Thus, in this case, both the conditions of (a) and (b) are fullfilled.
Similarly if we take,
A = non-origin point on L1
B = non-origin point on the line of intersection of π1 and π2 and
C = non-origin point on L2.
If we take A = C'', B = B', C = A', both the conditions of (a) and (b) are fulfilled.