Incircle
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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. Quadrilaterals that do have an incircle are called tangential quadrilaterals.
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 .
- For any polygon with an incircle, , where is the area, is the semiperimeter, and is the inradius.