question_answer

If \[A({{x}_{1}},{{y}_{1}}),\ B({{x}_{2}},{{y}_{2}})\] and \[C({{x}_{3}},{{y}_{3}})\] are the vertices of a triangle, then the excentre with respect to B is [RPET 2000]

A) \[\left( \frac{a{{x}_{1}}-b{{x}_{2}}+c{{x}_{3}}}{a-b+c},\,\frac{a{{y}_{1}}-b{{y}_{2}}+c{{y}_{3}}}{a-b+c} \right)\]

B) \[\left( \frac{a{{x}_{1}}+b{{x}_{2}}-c{{x}_{3}}}{a+b-c},\,\frac{a{{y}_{1}}+b{{y}_{2}}-c{{y}_{3}}}{a+b-c} \right)\]

C) \[\left( \frac{a{{x}_{1}}-b{{x}_{2}}-c{{x}_{3}}}{a-b-c},\,\frac{a{{y}_{1}}-b{{y}_{2}}-c{{y}_{3}}}{a-b-c} \right)\]

D) None of these