If is a equalateral triangle of side a then find the minimum distance between two excentres ?
a
2a
Excenters of Triangle -
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
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Distance between any two excentres is 2a.
Note:-
The excentres of an equilateral triangle is equidistant from each other and this distance is twise of side of triangle
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