Right triangle A C D with right angle at C is constructed outwards on the hypotenuse \overline{A C} of isosceles right triangle A B C with leg length 1 , as shown, so that the two triangles have equal perimeters. What is \sin (2 \angle B A D) ?
Answer Choices
A. \dfrac{1}{3}
B. \dfrac{\sqrt{2}}{2}
C. \dfrac{3}{4}
D. \dfrac{7}{9}
E. \dfrac{\sqrt{3}}{2}