please tell the output voltage mathematically or graphically

@raja   what is the Vo at the point of change of slope ?
In book it is 4.65 V
My approach :
as long as the Vi is < 9.3 V , the diode D1 will be ON because in that case V_A will be < 10 V and current can flow through 10k resistor. And if this is true then D2 will also be 0N and Vo = Vi.
Now second interval i.e Vi > 9.3 V,  same reasoning for D3 i.e D3 will be ON as long as Vi > -9.3 V & D2 is ON & D4 is also ON. But in this case if we track from input to the output through D3 & D4 , then i get Vo = Vi and this is making D1 ON which i assumed to be OFF. Summarizing my results :

0<Vi<9.3       all diodes are ON & Vo = Vi
Vi>9.3     all diodes are ON & Vo=Vi.....  but this is not possible because this makes V_A > 10 which shows current can't flow from +10V battery.    So in short  i know i am doing but the question is where ????