Incircle

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Triangle ABC with incenter I, with angle bisectors (red), incircle (blue), and inradii (green)

An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. Every triangle and regular polygon has a unique incircle, but in general polygons with 4 or more sides (such as non- square rectangles) do not have an incircle.

Formulas

• The radius of an incircle of a triangle (the inradius) with sides and area is
• The radius of an incircle of a right triangle (the inradius) with legs and hypotenuse is