Consider angle XZY in the attached figure. It is always 1/2 the measure of arc XY, no matter where Z may be located on the major arc XZY. This is true even when ZY is very short.
Now, consider what happens when Z falls on top of tangent point Y. The angle is still half the measure of arc XY, still 62°.
Selection C is appropriate.
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I apologize for any confusion caused by my choice of Z as the name of the point I added. Nothing in my explanation is intended to refer to the Z already shown in the unmodified figure.
