Final answer:
DP equals 10 since P is the circumcenter of ΔABC and is therefore equidistant from all vertices of the triangle.
Step-by-step explanation:
To find DP when P is the circumcenter of ΔABC, we need to use the property that the circumcenter is equidistant from the vertices of the triangle. Since PC is given as 10, which is the radius of the circumcircle, DP must also be 10 because the circumcenter is the same distance to all three vertices (D, B, and C).
The information provided about AD and DB being 3x - 11 and 5x - 29 respectively seems to be irrelevant unless we are working with a larger context or seeking to find the value of x, which is not necessary for finding DP alone in the context of a triangle with a given circumcenter P.