Excenters of Triangle - Practice Questions & MCQ

Excenters of Triangle

An excenter is a point at which the line bisecting one interior angle meets the bisectors of the two exterior angles on the opposite side.

The circle opposite to the vertex A is called the escribed circle or the circle escribed to the side BC . If $l_1$ is the point of intersection of the internal bisector of $\angle B A C$ and external bisector of $\angle A B C$ and $\angle A C B$ then,

Coordinates of $\mathrm{I}_1, \mathrm{I}_2$ and $\mathrm{I}_3$ is given by

$\begin{aligned} I_1 & \equiv\left(\frac{-a x_1+b x_2+c x_3}{-a+b+c}, \frac{-a y_1+b y_2+c y_3}{-a+b+c}\right) \\ I_2 & \equiv\left(\frac{a x_1-b x_2+c x_3}{a-b+c}, \frac{a y_1-b y_2+c y_3}{a-b+c}\right) \\ I_3 & \equiv\left(\frac{a x_1+b x_2-c x_3}{a+b-c}, \frac{a y_1+b y_2-c y_3}{a+b-c}\right)\end{aligned}$