Final answer:
Without the accompanying figure and further details, it is not possible to determine the length of AD with the given information.
Step-by-step explanation:
The question asks to determine the length of AD given various lengths in a figure, namely AP, AR, AQ, AB, and AC. Unfortunately, without the accompanying figure, it is impossible to answer this question accurately. Without significant details about the geometric relationships within the figure, such as angles, types of triangles, or other shapes involved, we cannot determine the length of AD confidently. If additional details from the figure can be provided, such as relationships between the points or any special properties of the shapes, a solution may be formulated.