Methods: let BC=x,
Vector AP vector BC= (vector AC+ vector cp). Vector BC
= Vector AC. Vector BC+ vector cp. Vector BC
= 2 times angle ACB+2 times angle (180 degree angle bCB)
= 2 times angle ACB-2 times angle (angle bCB)
= 2x [(4+x2-9)/(4x)-(4+x2-16)/(4x)] Cosine Theorem.
=7/2=3.5