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3 Questions around this concept.
If one vertex of an equilateral triangle of side 2 is the origin and another vertex lies on the line y then third vertex can be
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 I1 is the point of intersection of the internal bisector of ∠BAC and external bisector of ∠ABC and ∠ACB then,
Coordinates of I1 , I2 and I3 is given by
$\begin{aligned} I_1 & \equiv\left(\frac{-a x_1+b x_2+c x_3}{-a+b+c}, \frac{-a y_1+b y_2+c y_3}{-a+b+c}\right) \\ I_2 & \equiv\left(\frac{a x_1-b x_2+c x_3}{a-b+c}, \frac{a y_1-b y_2+c y_3}{a-b+c}\right) \\ I_3 & \equiv\left(\frac{a x_1+b x_2-c x_3}{a+b-c}, \frac{a y_1+b y_2-c y_3}{a+b-c}\right)\end{aligned}$
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