Our Incenter Triangle Calculator helps you quickly find the exact coordinates of the incenter for any triangle. Simply input the vertices (x,y) and get the point where all three angle bisectors intersect. Ideal for geometry students, engineers, and mathematicians.
Formula:
The incenter `I` of a triangle with vertices `A(xA, yA)`, `B(xB, yB)`, `C(xC, yC)` is calculated using the side lengths `a`, `b`, `c` (opposite vertices A, B, C respectively).
`I = (Ix, Iy)` where:
`Ix = (a ⋅ xA + b ⋅ xB + c ⋅ xC) / (a + b + c)`
`Iy = (a ⋅ yA + b ⋅ yB + c ⋅ yC) / (a + b + c)`
The side lengths are found using the distance formula:
`a = √((xB - xC)2 + (yB - yC)2) `
`b = √((xA - xC)2 + (yA - yC)2) `
`c = √((xA - xB)2 + (yA - yB)2) `