Determining Vo in a circuit with diodes
When Vi>2.7, your diagram is correct. 

So ,Vo= (Voltage across the R2) + (Voltage drop across Diode = 0.7V)  + (Voltage from the DC                 source = 2V)

Use KVL to find the voltage across R2. 

Since it is effectively a voltage divider with a voltage , Vi - 0.7 - 2 =Vi-2.7

So the Voltage across R2 is , VR2 = ( Vi-2.7) (R2/(R1+R2)

So, Vo= ( Vi-2.7) (R2/(R1+R2))  +  2.7

Since R1=R2, it can be solved to 

Vo = (Vi+2.7)/2