In a right triangle \( \mathrm{ABC} \), right angled at \( \mathrm{A} \), on the leg \( \mathrm{AC} \) as diameter, a semicircle is described. The chord joining A with the point of intersection \( \mathrm{D} \) of the hypotenuse and the semicircle, then the length \( A C \) equals to
\( \mathrm{P} \)
(A) \( \frac{\mathrm{AB} \cdot \mathrm{AD}}{\sqrt{\mathrm{AB}^{2}+\mathrm{AD}^{2}}} \)
(B) \( \frac{\mathrm{AB} \cdot \mathrm{AD}}{\mathrm{AB}+\mathrm{AD}} \)
(C) \( \sqrt{\mathrm{AB} \cdot \mathrm{AD}} \)
(D) \( \frac{A B \cdot A D}{\sqrt{A^{2}-A D^{2}}} \)
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