If A B C is a triangle, then what is the value of the determinant | array ccc C & ~B & 0 ~A & 0 & ~B 0 & ( ~B + C ) & C array | ?

Step-by-step solution

| array ccc C & B & 0 A & 0 & B 0 & (B+C) & C array | aligned & = C[- B (B+C) & =- B C [ (B+C) (B+C) + A A ] & =- B C [ (B+C) A+ A (B+C) A (B+C) ] & =- B C (A+B+C) A (B+C) & = - B C A (B+C) =0 . aligned