The fault lies entirely with car A because, in encroaching onto the main road, it has caused car B to swerve and thereby colliding with car C.
The definition of a Road Traffic Accident is:
"Owing to the presence of a vehicle on a road an accident occurs..." (and it goes on to tell us how it can lead to a collision / damage can occur / injuries can be caused etc etc)
The accident would therefore not have occurred had the car on the minor road (Car A) not entered onto the main road until safe to do so.
In all probability, and assuming it was not fatal, it would not be unusual for the driver of Car A to be reported for careless driving.