In the diagram, secant AP¯¯¯¯¯¯¯¯ intersects the circle at points A and B, and secant CP¯¯¯¯¯¯¯¯ intersects the circle at points C and D. The lines intersect outside the circle at point P. A circle with no center shown and two secants as described in the text. Points A, B, D and C lie on the circle. Segment B P equals 6, segment C D equals 7, and segment D P equals 5. What is the length of AP¯¯¯¯¯¯¯¯?