Use our free Incenter of a Triangle Calculator to quickly find the coordinates of the incenter. Simply input the vertices (x1, y1), (x2, y2), and (x3, y3) of your triangle to get instant, accurate results for this important geometric point. Ideal for students and professionals.
Formula:
The incenter (I) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3) is given by the formula:
I = ((ax1 + bx2 + cx3) / (a + b + c), (ay1 + by2 + cy3) / (a + b + c))
Where:
- a is the length of side BC = √((x3 - x2)2 + (y3 - y2)2)
- b is the length of side AC = √((x3 - x1)2 + (y3 - y1)2)
- c is the length of side AB = √((x2 - x1)2 + (y2 - y1)2)
The incenter is the point where the three angle bisectors of the triangle intersect, and it is also the center of the triangle's inscribed circle (incircle).