Triangle wave input with Zener and diode
Rev A

Pardon my Senior's Moment where I got distracted on the question with 10Vpk and answered for 7Vpeak.  

here is the simulation for +/-10V pk.

Except I used 2 batteries to model the simple thinking of a diode switch voltage.

This is the kind of question that makes you doubt your answer. Why would they want to do this? Just to force you to think  about the threshold effects of diodes and use a simulator because the these assumptions have current requirements and the Zener currents for Vi=+10V are sub-milliamp (167uA) which means the Vz drops to 5V or even less, so your simple model is good enough to ignore the Zener for 0.1V tolerance (82 mV error with the assumptions in this circuit) so if you need more accuracy you need better Vi spec tolerances and don't use a Zener, use a band gap diode instead. (ha)

If this were an ideal 0.7V switch, Imagine  the 5V midpoint in the middle of the diode,D2   if the Zener was pulled out. 
 Thus A= 5+ 0.7/2 and C=4.65V= 5-0.7/2

Next you think , if Point A is 4.65V and the 5.1 Zener is replaced with a battery, you have an error in this because it is now pulling up the voltage with 167 uA of current  when it should be drawing about this much getting near Zener voltage. . So for brevity and 0.1V accuracy estimated, we can ignore the Zener for Vi=+10.  In reality it drops C voltage by 85 mV or so .

Purpose of Question:

  This teaches you , that you cannot always use KVL blindly and assume the Zener is a battery voltage when expected maybe to be conducting some current .

But for this question , you can still ignore the marginal effects of the Zener on voltage at C.



Original Answer

There are several ways to analyze it easily. Consider each diode as a 0 Ohm voltage source with a unipolar threshold of 0.7V and a Zener is a bipolar threshold of Vz=Vr and Vf =0.7 for both when the Anode is positive.


  The easiest way is to treat each diode, Vf or Zener voltage, Vr (or Vz @ Iz) as a 0 Ohm voltage sink with a switch when the voltage exceeds Vf or Vr and open circuit below that.




Ticky Tacky Technical Details

Although the reality is all diodes conduct logarithmically up to their rated continuous current as it's incremental impedance drops below the electrode bulk fixed resistance, Rs.  The Power continuous rating in Watts at 85'C  is inversely proportional to the diodes incremental series resistance Rs show as the curve to the right of 100mA in the graph below. It is curve on a log scale and linear slope on a linear axis

The incremental resistance, ΔRs of the diode is very high at low currents then rise to much lower resistance to be neglected for logical linear analysis. So we think of it as a voltage switch > 1mA. 

It doesn't matter much whether you use a different forward threshold of Vf= 0.6, 0.65 or 0.7 as you only need to estimate the result.  In the reverse,  Vr has a variable large  voltage rating like this part Vr=100  or a low voltage like the Zener 1N4733A = 5.1V @ 67mA . So you can think of the Zener as closed battery switch above 5.1V its reverse voltage rating but used as a positive value here. Then of course as a simple Silicon diode Vf= 0.7 V like D2.

Note that the cheap silicon diodes are also used as a disposable thermometer sensors with it's controlled NTC Negative TempCo characteristics.







simulate this circuit &ndash; Schematic created using CircuitLab

You can use 0.7 V , I might use 0.6V and it all depends on the diode current rating to determine minor variations at 1mA to 10 mA.  Either is acceptable but  for advanced user they want more accuracy so datasheet specs and accurate simulation with tolerances are included in the design specs.  For academic purposes either value is OK. 


  But for real design work specs and datasheets must be followed and this simulation indicates a result of 623 mV at 3mA.




As you may be learning to analyze intuitively, the Zener circuit has no effect on the output here, as point A never reaches the Zener voltage, nor point B.

If you read this far, you deserve to playing with the interactive simulation in your browser.