Since ZR is the bisector of segment XY, it divides XY into two equal parts. Given that the length of XY is 10 cm, the length of XZ (which is one half of XY) can be calculated as follows:
\[ XZ = \frac{XY}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \]
Thus, the length of XZ is 5 cm.
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