In circle O and circle P, AP is equal to 10 and AC is equal to 8. Line segment CB is also perpendicular to line segment AP. Find the measure of DP.

Here's what I have so far : Since all radii of a circle are congruent, triangle CBA is an isosceles triangle. And since base angles of an isosceles triangle are congruent, angle C and angle A are both equal to 45. After there, I guess I could use trig to figure out the measures of CB and go from there, but I think I'm going in the wrong direction.

Can anybody help me?