๐ Incenter Calculator
Calculate the incenter (center of inscribed circle) coordinates of a triangle.
Vertex A:
Vertex B:
Vertex C:
What is the Incenter?
The point where the three angle bisectors of a triangle meet. The incenter is equidistant from all three sides, and this distance is the inradius (r).
Incenter Coordinate Formula
I = (aยทA + bยทB + cยทC) / (a + b + c)
Here a, b, c are the lengths of the sides opposite vertices A, B, C respectively (a=|BC|, b=|CA|, c=|AB|).
Inradius
r = S / s
S = triangle area, s = semi-perimeter = (a+b+c)/2
Position of the Incenter
The incenter is always inside the triangle. This distinguishes it from the circumcenter.
Alternative Expression
r = (sโa)ยทtan(A/2)
r = (sโb)ยทtan(B/2)
r = (sโc)ยทtan(C/2)