Sum of angles BCD, BAD equals 180, so points A,B,C,D lie on a circle. Then angle ACD equals angle ABD, which equals 45 degrees, due to isosceles right triangle ABD. By the Law of Cosines: AD = sqrt(20), so BD = sqrt(2)*AD= sqrt(40), then BC = sqrt(AD**2-CD**2)= 4*sqrt(2)
Sum of angles BCD, BAD equals 180, so points A,B,C,D lie on a circle. Then angle ACD equals angle ABD, which equals 45 degrees, due to isosceles right triangle ABD.
By the Law of Cosines: AD = sqrt(20),
so BD = sqrt(2)*AD= sqrt(40),
then BC = sqrt(AD**2-CD**2)= 4*sqrt(2)