Difference between nominal operating point and optimal operating point of induction machine
For a general purpose motor, the nominal operating point is the speed and torque point at which the motor is producing the maximum torque at which it can operate continuously without overheating.

The optimum operating point would usually be the operating point at which the motor efficiency is maximum.

Ordinarily, the operating voltage and frequency would be assumed to be the nominal design voltage and frequency.

The circle diagram seems to be more about the limits of performance rather than continuous performance at a safe operating point. I don't know how it is useful in the context of rated operation.

The diagram below shows current, torque, efficiency and power-factor vs. speed for a typical polyphase induction motor. The full-load line defines nominal operation. At that point, the nominal speed is about 0.96 PU speed and peak efficiency occurs slightly about 0.97 PU speed, so the nominal and optimal operating points are quite close together. The torque curve should cross the full load line at 1.) PU torque but it doesn't.



Image from Alger, The Nature of Polyphase Induction Machines, 1951 General Electric Co.

Efficiency

To draw a circle diagram, you must have data from no-load, locked-rotor and DC resistance tests. From that, you can determine values for R1, R2, Rm,(X1+X2) and Xm. Then you can do the proper calculation for efficiency vs. slip for mechanical power developed in the rotor. I believe that you need to neglect mechanical losses. If you assume that the slip for maximum efficiency is also the slip for rated motor operation, you can determine the current and power factor for rated motor operation and show the rated operating point on the circle diagram.