A. $S = \frac{1}{2}ca$

B. $S = \frac{{ - \sqrt 2 }}{4}ac$

C. $S = \frac{{\sqrt 2 }}{4}bc$

D. $S = \frac{{\sqrt 2 }}{4}ca$

A. $R = \frac{a}{{\sin A}}$

B. $R = \frac{{\sqrt 2 }}{2}b$

C. $R = \frac{{\sqrt 2 }}{2}c$

D. $R = \frac{{\sqrt 2 }}{2}a$

A. ${a^2} = {b^2} + {c^2} + \sqrt 2 ab.$

B. $\frac{b}{{\sin A}} = \frac{a}{{\sin B}}$

C. $\sin B = \frac{{ - \sqrt 2 }}{2}$

D. ${b^2} = {c^2} + {a^2} - 2ca\cos {135^o}.$