‘Encontrar a’ vs ‘Encontrarse con’
 

I met your brother John in the city centre today (I bumped into him by chance):
• Hoy encontré a tu hermano Juan en el centro.
• Hoy me encontré con tu hermano Juan en el centro.

I met your brother John in the city centre today (I had already planned to meet him there):
• Hoy encontré a tu hermano Juan en el centro.
• Hoy me encontré con tu hermano Juan en el centro.

Are these sentences correct?

If so, is it safe to say that ‘encontrar a’ and ‘encontrarse con’ both mean:
(i) to bump into by chance
(ii) to meet as per previous arrangement.

Hi, fglorca:

Yes, both encontrar and encontrarse can be used for planned meetings and chance encounters. The a being referred to is the a personal, i.e., it isn't a preposition required by the verb itself like referirse a.

You can read some more on encontrar(se) in the DPD here.