A right triangle XYZ is inscribed in a circle with a diameter of 13 cm. An altitude from Y is drawn to the hypotenuse XZ. If the length of leg XY is 5 cm, what is the length of segment XH on the hypotenuse?

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1. By Thales, the hypotenuse equals the circle diameter, so $XZ=13$.  
2. For a right triangle with altitude to the hypotenuse, the projection rule gives $XY^2= XZ\cdot XH$.  
3. Plug in values: $XH=\dfrac{XY^2}{XZ}=\dfrac{5^2}{13}=\dfrac{25}{13}$.  
4. So $XH=25/13$ cm.  
FINAL_ANSWER: a

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