Triangle Incenter Finder

Calculate the incenter and inradius of a triangle given its three vertices. The incenter is the point where the triangle's angle bisectors intersect.

Vertex Coordinates

x₁

y₁

x₂

y₂

x₃

y₃

Incenter Properties

(1.000, 1.000)Point

Incenter Point (I)

Inradius (r)1.000

Perimeter12.00

Side Lengths

a5.00

b3.00

c4.00

What is an Incenter?

The incenter is the center of the largest circle that can fit inside the triangle (the incircle). It is equidistant from all three sides and always lies inside the triangle. It is the concurrent point of the three internal angle bisectors.

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Pro Tips

Incircle: The circle centered at the incenter is tangent to all three sides.
Internal: Unlike other centers (like circumcenter), the incenter is ALWAYS inside the triangle.
Distance: The distance from the incenter to any side equals the inradius.

Fun Facts

"Incenter coordinates are the weighted average of the vertex coordinates, with weights equal to opposite side lengths."
"The area of a triangle can also be calculated as Area = s × r, where s is the semi-perimeter."
"Every triangle has exactly one incenter."

Formula: I = ( (ax₁+bx₂+cx₃)/(a+b+c), (ay₁+by₂+cy₃)/(a+b+c) )

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