12.1.14 Olympic Geometry

Condition: quadrangle \ (a b k d \) is inscribed in the anniversary \ (\ omega \) radius \ (\ sqrt {37} \). On the side \ (k d \) the point \ (c \) is chosen so that \ (\ angle b c d = 90^{\ circ} \). Circle \ (\ omega \) radius 6, described around the triangle \ (b c k \), applies to the segment \ (a d \) and applies to the line \ (a b \). Find the length of the segment \ (a b \), angle \ (b a d \) and the area of the quadrangle \ (a b c d \).