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In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. The center of the incircle is called the polygon's incenter. An excircle or escribed circle of the polygon is a circle lying outside the polygon, tangent to one of its sides and tangent to the extensions of the other two. Every polygon has many distinct excircles, each tangent to one of the polygons sides. See also Tangent lines to circles.

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  • Inscribed circle
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  • In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. The center of the incircle is called the polygon's incenter. An excircle or escribed circle of the polygon is a circle lying outside the polygon, tangent to one of its sides and tangent to the extensions of the other two. Every polygon has many distinct excircles, each tangent to one of the polygons sides. See also Tangent lines to circles.
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  • In geometry, the incircle or inscribed circle of a polygon is the largest circle contained in the polygon; it touches (is tangent to) the many sides. The center of the incircle is called the polygon's incenter. An excircle or escribed circle of the polygon is a circle lying outside the polygon, tangent to one of its sides and tangent to the extensions of the other two. Every polygon has many distinct excircles, each tangent to one of the polygons sides. The center of the incircle can be found as the intersection of the many internal angle bisectors. The center of an excircle is the intersection of the internal bisector of one angle and the external bisectors of the other two. From this, it follows that the center of the incircle together with the many excircle centers form an orthocentric system. See also Tangent lines to circles.
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