Cyclic quadrilateral A B C D satisfies \angle A D C=2 \cdot \angle B A D=80^{\circ} and \overline{B C}=\overline{C D}. Let the angle bisector of \angle B C D meet A D at P. What is the measure, in degrees, of \angle B P D?
Cyclic quadrilateral A B C D satisfies \angle A D C=2 \cdot \angle B A D=80^{\circ} and \overline{B C}=\overline{C D}. Let the angle bisector of \angle B C D meet A D at P. What is the measure, in degrees, of \angle B P D?