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Circle \( \mathrm{C}(\mathrm{O}, \mathrm{r}) \) touches the circle \( \mathrm{C}\left(\mathrm{O}^{\prime}, \mathrm{r}^{\prime}\right) \) internally at \( \mathrm{A} \). \( \mathrm{AB} \) is a chord of larger circle which intersects the smaller circle at \( \mathrm{P} \), then \( \mathrm{AP}: \mathrm{AB}= \)
a. \( \frac{\mathrm{r}^{\prime}}{\mathrm{r}^{2}} \)
b. \( \frac{\mathrm{r}^{\prime 2}}{\mathrm{r}} \)
c. \( \frac{r^{2}}{r^{\prime 2}} \)
d. \( \frac{\mathrm{r}}{\mathrm{r}^{\prime}} \)
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