A) \( \Large \frac{ \left(ax_{1}-bx_{2}+cx_{3}\right) }{a-b+c},\ \frac{ay_{1}-by_{2}+cy_{3}}{a-b+c} \) |
B) \( \Large \frac{ \left(ax_{1}+bx_{2}-cx_{3}\right) }{a+b-c},\ \frac{ay_{1}+by_{2}-cy_{3}}{a-b-c} \) |
C) \( \Large \frac{ \left(ax_{1}-bx_{2}-cx_{3}\right) }{a-b-c},\ \frac{ay_{1}-by_{2}-cy_{3}}{a-b-c} \) |
D) none of these |
A) \( \Large \frac{ \left(ax_{1}-bx_{2}+cx_{3}\right) }{a-b+c},\ \frac{ay_{1}-by_{2}+cy_{3}}{a-b+c} \) |
We know that, if the vertices of a triangle are \( \Large A \left(x_{1},\ y_{1}\right),\ B \left(x_{2},\ y_{2}\right)\ and\ C \left(x_{3},\ y_{3}\right) \) and the respective sides are a, b and c, the excentre with respect to angle B is
\( \Large \left(\frac{ax_{1}-bx_{2}+cx_{3}}{a-b+c},\ \frac{ay_{1}-by_{2}+cy_{3}}{a-b+c} \right) \)